The Devs have mentioned that they will add Captains quarters & so on to ship interiors. We'll just have to wait for it. There's plenty to fix and do before that should be a priority though imo. That being said, I'd love to see them added as well!
Just thinking long term, I could imagine they could do something like renting personal quarters on Starbases, like housing, or even player starbases you can walk around with. Or maybe the personal quarters would be on the ships, that would make sense also. You could upgrade a ship with things like 10-Forward or Holodecks where you could play a online computer game LOL.
Things like that make a good money sink to balance economies, and usually come along later in games.
Edit: Actually if they ever added game within games like some games, the holodeck would be a logical place to do that. 3 D Chess, or one of the training things from Enterprise Series.