Nassau, Bahamas: Been there, done that, bought the T-shirt. We have been here four times,; in 2000, 2001, 2005, and 2010; and I cannot think of any reason to go back. In reality, after you visit the Atlantis Resort - which is a must-see, there is not a whole lot to do here, which is quite surprising as often there will be 3 to 5 cruise ships in port. As I previously mentioned, the last time we were at this island, we stayed on board and enjoyed the pool to ourselves.
Atlantis offers many activities, from dolphins, waterpark, casinos, or simply a day on the beach. One exhibit you should visit while at Atlantis is called "The Dig". It's a "what-if" exhibit depecting what the real Atlantis might look like should it ever be discovered, complete with vintage "20,000 Leagues under the Sea"-like apparatus. By far the best attraction I believe is the The Dolphin Encounter is rather expensive, especially if you purchase photos. There are dolphin encounters in several of the Caribbean islands other than Nassau, and its usually less expensive at another island. Nassau, in a sense is a rookie port - as it's on the 3 and 4 day Bahamas cruises, and is often the first port many folks visit.
Atlantis is on Paradise Island, and the easiest way to get over to the island is by water-taxi. Its usually quicker (and safer) than taking an automobile taxi. The water-taxi's fare is usually only a couple of dollars, and they pick you up and drop you off adjacent to the cruise ship dock. Taxi's make a round trip run about every 1/2 hour or so.
Nassau has one of the largest cruise ship facilities, and it's not unusual to see 5 ships in port on one day. It is one of the few ports that can handle Royal Caribbean's Oasis and Allure mega-cruise ships. This photo is in 2000, right after the port was modernized. Of interest is the ship to the right; the defunct Premier Cruise Line. Of equal interest is that the ship didn't have bow-thrusters, and needed tugs to help it get underway.