Hi, the atlantis doesnt allow you to use the beach, but you can go in and walk past the free portion of the aquarium (which was great) or pay and get to go/see through the whole aquarium. If you want to use the casino, anyone 18 or over can go in and gamble to their hearts content. If you would like to go to a beach on paradise island, there is a public beach to the right of the Atlantis next to the Riu Hotel.
Make sure you get a frozen drink at the dock when unloading at Paradise Island (if using water taxi). They are to die for. And if you like Conch Fritters, the Fritters at Conch Fritters Bar and Grill are the best ones I have ever had. The Chowder is a must try too.
The Pirates Museum is reasonable and a good time could be had by all ages. You could also walk around the straw market or go to the top of Fort Fincastle. Its free I think, and all you'll have to do is tip the person up there telling you a little history about the island. You can see forever, and the great views of the port and city are excellent picture opportunities.
Enjoy, I enjoyed Nassau more than most, and thought the Nassau citizens were all very nice.