In my head, it's in a similar style as the game "Rock n' Roll Racing". There are alien planets and all kinds of weird personalities. It could play in the future where Earth has a different nickname, like "that vile piece of crap nobody cares about anymore".
I thought of simplifying it by displaying a galaxy on one screen (similar to the world map in "Ports of Call").
You can buy various spacecrafts and hire pilots (like the character selection in "Rock n' Roll Racing").
You must assign them to various starting planets, manage their income, motivate them with special gifts, etc.
Your taxi company focuses only on getting people from planet to planet, you don't care about specific cities (that's the client's problem). There could be shuttles in the orbits of the planets, or if it's a godforsaken planet, maybe there's a special event that your pilot is required to land somewhere, asking you for a decision.
It should all be very random and funny: Pilots could be slime balls with weird attributes like, "doesn't like planets close to the sun". Customers could set strange goals or be totally racist and not want to drive with slime pilots.
There would be random events, like customers not paying and running away, or attempting to kill your pilot, or stealing your vehicle (which means you should add some security measures).
Random events, characters and planets could borrow from the vast amount of sci-fi tropes, and reference and make fun of all kinds of sci-fi movies.
Time is a weird factor in space, since you can't have "monthly" costs, but maybe it's simply a regular upkeep. If a taxi needs repairs, you repair it. A driver's income is a percentage based on what every successfully delivered customer pays.
Goals could be simple, such as having to bring a hundred clients to their target destinations, before a competing company does. Or use only the crappy taxis to deliver ten customers to a far (far) away galaxy. Or you need to rescue a customer from a planet full of giant ants, only to realize the customer is a giant bee, so your pilot should probably not be allergic.
(And yes, I realize there's a "Space Taxi" in a certain German movie, I would like to ignore that... xD)