The extra dimension of space makes a huge difference to the more usual two-dimensional mapping and travelling that people generally engage in. Even a multi-level dungeon with two-dimensional levels connected by stairs and ramps is nothing compared to the full freedom of three-dimensional navigation.

Mapping three dimensions for a game is non-trivial. You can record star system coordinates as Cartesian triplets and calculate distances using Pythagoras's theorem, which will do the job, but visualising the "map" is tricky without complex graphing tools.

Various people have used tesseracts as dungeons, notably the original Baba Yaga's Hut adventure published in Dragon magazine #83, but these are generally just two-dimensional maps with macro-geometry folded in four dimensions. But imagine setting a game in a four-dimensional (or higher!) space, where the heroes can actually travel not only east, west, north, south, up, down, but also some other set of mutually perpendicular directions.

Transcript

[SFX]: Wooooooooooosssshhhh!! {Vader watches the Falcon enter hyperspace}
Admiral Piett: Well... that's interesting.
Admiral Piett: Did you turn the beam on?
Lieutenant Venka: Yes, sir!
Admiral Piett: Did you know in space there are six cardinal directions? And having your limbs tractor beamed in them might be quite—
Darth Vader: They escaped the beam.
Admiral Piett: Interesting fact: To break free of our tractor beam they'd need a power source bigger than this entire Star Destroyer.
{beat}
Darth Vader: They have the Lost Orb of Phanastacoria.
Admiral Piett: I seem to recall that you lost that, sir.
Darth Vader: Not any more. {walks away}