Sorry to say, but in my opinion, Nassau has very little to offer. The Atlantis used to be great, but now they charge big bucks to get in. You probably should look for a beach. Last week the Explorer never made it in to Nassau. Winds or tides were a problem.
It's not my favorite port, either, but there's still stuff to do. Walk around the shopping district and go to the straw market-- but beware that the vendors tend to descend upon you mercilessly! Ask how much, offer half that much, and take it from there. You can get some pleasant souvenirs cheaply.
Take the water taxi ($3 pp, but frequently an unsolicited "tour guide" will pass around a hat onboard) or regular taxi ($4 pp, but the water taxi is more fun) to Paradise Island. There *are* still some free beaches-- I just can't tell you where they are... but be prepared to do a decent amount of walking from the water taxi pier to the beach area. Actually, a regular taxi driver might take you all the way to the beach for the $4 pp... I'm not sure. But the beach there is lovely, in spite of the fact that the Atlantis keeps encroaching on more and more space. Don't bother trying to tour it-- they charge $25 pp to see the good stuff (like the aquarium and archeological digs).
Alternatively, take a taxi to Cable Beach. I haven't been there, but I understand there's a public beach that's not bad (but not as pretty as the one on Paradise Island). I'm sure they can tell you on the ship how much a taxi there would cost.
If this is your first visit, take the horse buggy ride that you'll find right near the docks. It's about $ 5.00 pp and lasts 15-20 minutes. It gives you a "quickie tour" and is relaxing and romantic. Nearby, you'll see the Visitor's Bureau. They can give you a map for a walking tour that takes you to the Queen's Stairway, Fort Fincastle, The Water Tower, the Post Office and Government House, and then to the Straw Market. You can do the whole tour in a little over an hour! When you get to the Straw Market, go to the upper level, where you'll find the best frozen thingees in the Bahamas.....