Congrats on doing your first cruise! You will absolutely love it especially it being Disney and the new Dream the Disney Dream!
As for what to do in Nassau, there are many different things to do and see. Of course you can go to Atlantis and do the tour of the aquarium which is nice. I would not do the water park. You can also do the casino or shopping there if you want. I like going to the rum cake factory to watch them make them, sample them and shop. I might walk through some of the side streets to see the shops as well as to see the Queens staircase and the gardens. Other than that I really do not get of the ship that often anymore. I might just to stretch and to get a shell or rum cake but that's it. Just get off for an hour or so.
If you stay on the ship, which is mostly what I do, I like to go to the movies, the spa (prices for spa services are cheaper due to being in a port), the cove cafe for coffee or just walk the ship. You can also do the art auction or other things that are planned on the Navigator.
This might sound funny but I like to go to the shopping presentation on the very first day prior to the ship leaving port. I get all the coupons with whatever freebies come along with them. then when I get into Nassau I get off the ship and go Left (something you will hear a lot of) and shop in the stores spending the littlest that I can while getting all the free stuff. It is just something that I can do on land to stretch and I love getting free stuff which I can give as gifts!
Whatever you do enjoy every minute of the cruise and the Disney Dream!
Have a DREAMfilled cruise!