They're really not that different...

...because you left out an important adjective: abandoned.

Often, those "fantasy" adventure locations you cited - a crypt, a prison, a cave system, a necromancer's lair, or a castle - are only interesting because nobody is currently and legitimately/legally living there. They're full of loot because it's stuff that was left behind when whomever built the place departed. They're generally not being used for their original purpose.

For example, crypts are places the dead are buried. If those dead folks have families who are not equally dead, it's entirely likely that there's no loot and no monsters, because relatives keep their family's resting place neat, clean, and secure. A necromancer usually doesn't have a "lair" because he built it, but because he found it, and he only found it because somebody else left it behind.

If you want to have a similar looting type experience in a non-fantasy game, you have to use similar abandoned locations. To use another of your examples, an active prison in both fantasy and science-fiction games is going to be filled with prisoners and guards. It is going to have a logistics organization - deliveries of food, drink, medicine, and so on. In either setting, it's good for a stealth/infiltration kind of mission.

An abandoned prison is a different story. You have to ask yourself why is the place no longer in use? Somebody built it where they built it for a reason, filled it with prisoners, and employed a staff of guards. Why did they stop? Where are the prisoners? Where are the guards? If the guards are gone, but the prisoners are not, why?

In your case, the bigger difference in feel is not about the fantasy/sci-fi split, but the source of authority. For the most part, fantasy adventurers are independent contractors - they take the jobs ("quests") they want, and ignore the rest. When the characters are regularly working for an organization, their end goal is always making the boss happy - they're collecting a paycheck, not loot.

It swings back around to asking those "Why?" questions. The interesting elements come more from the roleplaying about the characters motivations than blowing the heck out of things. I'm not just talking about the player characters either. Why is their boss sending them on these missions? How does his boss feel about it? If they're government, what do the people of their country think about what they do? These are the elements that make a "highly sponsored" or "well funded" game tick. There are a plethora of non-combat scenes that you can get out of delving into the motivations of the involved parties.

And of course... none of those questions are science-fiction specific.

...when you know why your locations are even worth an adventurer's visit.

Not all dungeons have walls.

A dungeon is really an encounter graph with connections between them. Encounter graphs can be generated without any walls.

You can start an encounter graph with a goal or a hook. A goal is an "end room" to your encounter graph (the treasure room of the moon king) while a hook is an entrance room to your encounter graph (a strange door with symbols on it on the side of a hill, glowing with magic as the moon shines on it).

In a dungeon, the graph follows the shape of the tunnels in the ground. Without that, you have to find other means to connect encounters.

One way is to connect them with information. You can see this in many films; the protagonists want to do X. One or more of them comes up with an idea (knowledge check). Some are ruled out, and some are attempted. Which leads to an encounter.

That encounter leads to other nodes. Often there are explicit choices.

Railroading is avoiding by making sure there is always more than one choice available, and more than one route to the goal (which could be a mirage) or to resolve the plot. Some of the choices could result in dead ends/side quests/plot hooks for another adventure.

We might start with a hook that implies a goal; a contract from an old contact to smuggle some cargo to old Earth.

[Contract (hook)]

...

[Deliver cargo]

now, old Earth has some security. So we have an intermediary goal:

[Contract (hook)]

...

[Find a way to avoid customs]

...

[Deliver cargo]

Maybe there are a few ways; corruption (bribe your way past customs), hacking (convince Earth security that you are cleared) and sneaking (get through customs without anyone noticing you).

[Contract (hook)]

...

Means of: [Corruption]     [Hacking]    [Sneaking]

...

[Deliver cargo]

In each of those cases, you are going to have to get information. Either find the right way to provide bribes, the right hacker or ice to penetrate Earth security, or a hole in the Earth custom's security fence.

[Contract (hook)]

       |

       +----------------+---------------+

       |                |               |

[Government contact]  [1337 Haxx0r]   [Smuggler's Asteroid]

 ...

[Corruption]          [Hacking]       [Sneaking]

...

[Deliver cargo]

We can now drill down to one of them. The government contact doesn't want to communicate electronically, so arranges to meet you at a resort.

[Contract]

    |

[Resort]

    |

[Government contact]

    ?

[Corruption]

at the resort, shenanigans can ensue.

The Haxx0r needs access to a specific security module.

[Contract]

    |

[Haxx0r]

    |

[Security module]

    ?

[Hack Earth Security]

those security modules are found on Earth cruisers. But you don't have the firepower to take one out; however, a cruiser was lost in the Styggian Abyss and not yet recovered.

[Contract]

    |

[Haxx0r]

    |

[Cruiser in Stygian Abyss]

    |

[Security module]

    ?

[Hack Earth Security]

but where is it? Well, you have a government contact; or, you could find an underworld contact who might know where it is.

The government contract might only work if you can get past the formal customs barrier, which requires sneaking through it. So you'll also have to do the Smuggler's asteroid subquest.

The smuggler's asteroid can have its own encounter graph.

The goal now is a series of options. Each of them actually ends up requiring you to explore 2/3 of the encounter graph (sometimes we recycle parts; if you go corruption, the government official is for finding someone to bribe; if you go haxx0r, the same official encounter graph (if not the same official) is for finding the location of the cruiser).

Keep adding choices and complications to the graph until the "dungeon" is large enough. Include mini-graphs (for the resort, the smuggler's asteroid, and for the cruiser); these mini-graphs can be reused for a related purpose later (much like you might recycle a dungeon layout you didn't use).

There are tracks, but there isn't a railroad, because there is more than one choice. You inform the players of their predicted results of going one step down each path, but not always about later consequences. And maybe some of the choices are dead ends (the smuggling route won't work, because the smuggler boss is maintaining strict secrecy about the hidden routes into Earth space, but by going that way you do a favour for a crime boss they aren't able to repay; treasure)

Human(oid)s will be human(oid)s

When in a scifi setting, what is new and innovative to us, is ordinary to the characters. People tend to iterate and adjust ordinary stuff.

Your problem is not that space stations won't have strange nooks and crannies, it's that new space stations won't have them. Just like that new crypt didn't have any at the time of the first ritual sacrifice: it just had the offering room. But then one of the less devout priests went corrupt and built in a hidden room where he stashed away his bribes. On the space station one of the cooks didn't think the pantry was big enough, so he re-compartmentalized a part of the hallway, blocked if off with improvised walls and immediately added a storage space for contraband. That malfunctioning airlock was obviously part of the original design, but also functioned back then. When the gang of space pirates captured the ship, however, they used it as an execution mechanism to expel mutineers into open space.

Secondary objectives and incomplete information

The first thing to remember is that you can technically do exactly the same in sci-fi as you can do in fantasy. Why not put the tomb of a long dead race as something they can explore?

But if your goal is to have them explore the given location more beyond them just making a beeline for the objective you can do this in multiple ways.

Optional/Secondary Objectives

By giving them secondary/optional objectives at the start they get the option or the need to explore more of the area then if they just headed straight for the objective. Rewarding them with better loot or info or help with the main objective are all ways to use positive reinforcement to get them to do the exploring automatically.

giving them these objectives only if they trigger something during the mission or find a clue of it while heading for the main objective also makes this feel natural and rewards exploration even while heading for the main objective.

Incomplete/Incorrect information

The other part is that apparently the players do not feel a need to explore. This probably means they know exactly where they are heading. The easiest way of getting them to brake this pattern is to start feeding them incorrect and or incomplete information. For instance if they have to secure object Alpha but nobody knows where it is or it turns out not to be in the place they thought it would be forces them to go looking for it and they will have to look in every room with maybe some clues here and there where the object is.

Different playstyle

Last thing to remember is that it could be that the players actually like playing these single minded soldiers who head straight for the objective and do not want to go exploring and puzzling everywhere. Discuss this with them as in this case you have different expectations of the game. If they really want to do the straight forward: plan, get in, execute mission, get out game that is not bad but you might have to adapt. You can still use the tips as mentioned above but you can also make it tat they have to do world exploring just to get the info for their planning Fase.

I agree with and second everything T.J.L. said - in particular, the importance of providing a "Why". However, while he emphasizes the significance of abandoned places (which I second), I think you can get much of what you want in a fully active target if you just reflavor a few things.

Active installations are likely to have dead ends, storage areas, and traps just for different reasons and slightly reflavored.

Any large industrial or military installation is likely to have reasonable analogs to everything you want in fantasy.

A large facility will have dead ends for many reasons. Some may be there because construction hasn't finished yet so that part just stops. A facility that was recently damaged by a natural event, disaster, or attack, may have parts blocked off. Some may have dead ends just because the designer was incompetent. You can find some really odd architectural choices in industrial and military buildings that come about either because of hasty design and construction or because of remodeling that had a limited budget and had to make the best of what was available.

Outside of the rare secured storage facility such as the famous Fort Knox, you probably won't find a random treasure room. But you could readily have storage rooms with neatly lined racks of valuable weapons or equipment. In a sci fi setting, that might include prototypes or even data storage devices.

The kind of traps that are common in fantasy likely won't exist in a sci fi setting, but analogs will. Few modern facilities use traps, but alarms are common and functionally equivalent if they trigger a rapid response force. Other hazards that need to be dealt with as if they were traps might be present. Doing the wrong thing in a lab could release noxious chemicals or radiation, properly securing that to avoid the result is not that different from disarming or avoiding a fantasy style trap.

PC and NPC desires can create dynamic interactions

I think these answers provide a lot of benefit to making things more dynamic but I wanted to approach this from a PC/NPC dynamic. The dungeon map can always be made dynamic with some consideration towards the whole idea of abandonment (e.g. a broken steam vent is barring passage here or this area has a massive tear that has vented the whole area and now the hatches are sealed or like DonFusili suggested about unauthorized additions to craft). However, PC choices and NPCs can have a major role on making a game more dynamic.

The BBEG has motivations

Say your party pulls up into orbit around an abandoned space station where Scientist I.R. Badguy was last seen. Well he probably sees them too. So he probably sets up traps and defenses as well as stashes of his precious "Kill All Life" files and then he will probably (depending on how cowardly he is) find the nearest warp capable escape craft. That might just be your ship so just in case he also sets up a Warp Jammer that he has the remote to in the "conveniently far away" communications center. And to make doubly sure you can't just track him down he blacks out Bioscanner signals with the same Jammer. So that 3d holoscan of the ship is meaningless because when the party steps into a trap they'll immediately question the whole map.

Other groups have motivations

So I.R. Badguy wasn't really that smart. Your party found him hiding in a supply closet in the hallway outside the docks. But now, you get a communication from "totally not evil syndicate" that wants him and the party's lives are negotiable. Oh and if you could kindly find all those "Kill All Life" files in the next hour that would be just great.

The Clock

Some of the best ways to make things dynamic is to make the PCs run on a clock. If you've watched the show Critical Role you see how tense everything gets when Matt Mercer pulls out the hourglass. When players have all of these objectives and side objectives and the clock is ticking they start acting very creatively in how to spend time most efficiently (sometimes least efficiently).

The Twist

So you show up bust down the door and get all the things done. Scientist I.R. Badguy is in your custody all his "Kill all Life" files are in a secure flash drive. You've saved the day. But Badguy just won't stop shouting how you need to let him go. The "totally not bad government" is trying to have him killed because his "Kill all Life" files are from their blacksite stores in Gamma Quadrant.

Basically, what happens when you give your PCs conflicting information. Even at the end of the mission you can have branching paths show up. Maybe the Bad Guy isn't really the bad guy you should be after. Or maybe, he's not the bad guy you are after and he's just a body double. Be careful with this because it can feel like you're cheating players of good rewards but when you do it well it makes a lasting story scene.

Other answers cover the space station "problem" really well (tl;dr: a space station is just a dungeon in disguise, especially if it's abandoned). I won't repeat what others have said about that, and will instead just concentrate on this part of your question:

The players have a fully functional ship and a government body that is sponsoring them, which seems like it was a mistake in hindsight, as it removes their motivation to explore or do anything other than their assigned mission.

I am reminded of video games like Deus Ex, where the player gradually discovers that the agency which they are working for is not what they thought. Or perhaps the PCs are working for your universe's equivalent of the Galactic Empire in Star Wars, and those "Rebel scum" they keep fighting against... wait... are they actually the good guys?

Keep giving them missions, but make the mission goals something they might think twice about - capture the Princess of Alderaan? But Alderaan is peaceful, and she has diplomatic immunity! Will they complete the mission anyway? What happens then? Will they let the Princess go - if they do, will they lie about it to the mission-giver - and if they lie, will their lie be believed? Perhaps they will even decide not to accept any more missions, and join the Princess in her battle for freedom instead! Whatever they choose, let them do it... whatever the consequences may be.

You mentioned space stations, but you could expand the possibilities by using a variety of other settings, then mixing them with a variety of mission types. The trick is to pair a clear mission with a challenging environment that requires nonlinear exploration. For example:

Assassination: A bunch of bothersome miners are rebelling on a corporate-owned asteroid. They've taken it over, and are led by a charismatic ex-marine who knows guerrilla tactics and never stays in one place. The PCs have to infiltrate the asteroid, blend in, and gather information as they explore the myriad tunnels and substations inside the hollowed-out asteroid. They can then plan the details and attempt to assassinate the leader, or (if the corporation is the real baddies) turn coat and help the miners.

Transport: After a particularly difficult mission, the PCs are given a simple transport mission. Just ferry some supplies from one out of the way planet to another. But things go wrong when their small transport ship is taken over by a vastly larger combat vessel from an unknown civilization. The PCs have to escape detection as they move through the massive alien vessel, trying to understand who they are and what their intentions are. Then they have to get word back to human-controlled space and get out with their lives.

Survey: Newly-discovered planets are often handed off to private contractors for survey. If the survey team finds anything valuable on the planet, generally in the form of natural resource, the team can get a big payday. But survey missions can be quite dangerous. Go in fast and dirty and they may wind up like the losers who ate it in the infamous TG-4459 mission. It's better instead to be careful and explore everything. And when the PCs come across a long-dead city, they'll want to make sense of it. What was the tech level? What were the aliens that inhabited it like? Are there possibly technological artifacts hidden in the ruins? And when they find some of those artifacts, what if they can't control them once they're awakened?

Reconnaissance: The war has been going on for too long. Destroying cities and wiping out continents, making space travel hazardous, and strangling trade. The corporation needs to find a safe jump path through the war zone. They send the PCs to explore a series of independent spaceports to determine whether they're likely to remain neutral. The PCs have to meet with port leaders, snoop around the port facilities and bars, and look for signs of influence from the combatants. When they discover that one side is using spies to turn the politics of one of the spaceports, the PCs have to root out the spies and neutralize them.

Rescue: On a moment's notice, the PCs are sent to a densely-populated capital planet in order to rescue a very important company executive. He's been kidnapped by an unknown party and taken to a sprawling favela. The PCs enter the favela and encounter a criminal underworld that is very hostile to outsiders. They have to quickly learn who is who in the favela, which criminal factions hold power, who hates who, and exploit that in order to gain information about where the executive might be. When they enter the long-dormant munitions plant where the exec is being held, they discover to their dismay that the plant is full of booby traps, automated defenses, and jury-rigged surveillance. They have to explore the plant carefully, figure out where the exec is, and get him out without getting him killed.

The previous answers are very good and they address the 'Space Dungeon' problem and the 'Diversity of missions' problem. However, there's one problem that isn't addressed: the setting itself.

Unless your PCs are the people in charge, they will expect to have little to say about what to do and where to go, about the missions and such, and having such a powerful back-up leaves little day-to-day struggle to include in the adventures. Plus, when they get 'missions', players will tend to stick quite strictly to the 'it's the mission' mindset and ignore everything else, even more when they play soldiers.

So, maybe you should consider changing your setting?

As an example, I've run two Star Wars campaigns over the years: one with the PC being your run-of-the-mill ragtag band of people in a ship, trying to survive and sometimes working for the Alliance, mostly to piss off the Empire. The others had the group all be part of the SpecForces, the special operations of the Alliance, going on the mission were Alliance Command would send them. The two campaigns were absolute opposite in terms of involvement from the players.

The SpecForces expected to have little liberty. They followed orders, went where they were sent, did the mission, came back to base, waited for the next mission, rinse and repeat.

The band of 'Free Entrepreneurs' was way more active, had way more social interactions between characters (up to the point that two of the players had their character become an item and make out in-game) and they were always on the lookout for ways to earn credits in order to keep living a bit longer.

I cannot count the number of time I ran a session based nearly completely on what the players wanted to do. We'd go from the end of the previous session, and they'd discuss what to do next, where to go, who to contact, etc, and I would go from there and give them what they wanted. Of course, that requires being good at improvising and knowing your universe.

So, maybe you should consider altering your setting to give your players more reasons to be involved and give you more liberty to throw them a lot of curve balls.