If you've never been to Nassau before you might want to find a tour that goes to Fort Charlotte and the Queen's Staircase. In my opinion, both are great historical sights for your first visit. There will probably be some other sites thrown in too such as Fort Fincastle and the Water Tower.
You can also visit Atlantis. I've been there but only in the lobby to the parts where you don't have to pay. You can buy day passes but I don't know how much they are - just that they are pretty expensive. Even if you don't go to the pay parts, a lot of the tours include a stop there and it's pretty neat to see. There's a huge aquarium inside that we enjoyed. I don't think you can use there beach for free, but I've heard there's a public beach pretty close.
If you're traveling with kids (or if you just really like pirates a lot), there's a pirate museum. If memory serves, it's really near the port - within walking distance. I've been through it and enjoyed it, but I wouldn't do it again.
If you're not traveling with kids, Senor Frogs is always a fun way to end a port day there. There's also the International Market or Straw Market...can't remember exactly what it's called. I've heard that you can get pretty good bargains there but It's WAY to crowded for me so, while I've been there twice, I just couldn't stay in long enough to actually buy anything.
I hope this helps!