At home - sit by the pool & read a good book, play with the baby, surf PPRUNE
Down route - if it's a nice town, the crew are a sociable lot and the schedule permits sufficient recovery time, then yes I do endeavour to hit the town for a few beers. Happens less than you'd think though, even with long haul.
If it's a short turn round, captain's a w***er / cabin crew antisocial, or most probably because the destination is a 3rd world sh!t hole like Dhaka or Lagos where you wouldn't go out anyway - then just kick back in the hotel room, catch up on sleep, go to hotel gym or swimming pool, eat room service nasi goreng, and play a lot of Halo on my nice new Dell XPS