When I worked on a liveaboard, I had several options:
When we were based out of Ft. Lauderdale, I would often crash at my parent's house in Miami or travel up to cave country in north central Forida and camp/cave dive.
Our company also provided a crew house (one in Lauderdale, one in Belize, depending where we were departing from). Very sparse accommodations-not my first choice.
I also did a lot of traveling during my off time. When we were based in Belize, I would often travel for three or four weeks at a time--it gave me an opportunity to go to Nicaragua, Guatemala, El Salvador, Cozumel, and Akumal. If you stay in hostels and eat like a local (not in the tourist restaurants), and take buses this was an inexpensive yet awesome way to get to see the world.