When I was there, we pretty much stayed on our resort, but the one time we left, we visited the Ardastra Gardens Zoo. They didn't have a lot of exotic animals, but their flamingo show was really cool, and made the trip worth it. They also have huge birds that will sit on your head, lol. You can get a pic of yourself with a bird on your head for free. It was a fun experience.
Some of the things you can engage in include visiting the marine habitats, the paradise island, the Blue Lagoon Island or take a tour of the Versailles garden. You can also go climbing the Queen's Staircase or see the Pink Buildings in Parliament Square. Check the tour guide or visit http://www.nassauparadiseisland.com/what-to-do/ for more details.