I took the Fantasy to Bahamas in 2001 and went back there again last year on Royal Caribbean. On the Fantasy we booked through Carnival the Blue Lagoon tour, which was about $40 or $45 per adult. Pretty expensive, but the Blue Lagoon is a beautiful little island where you spend the day and get food. It is paradise there. You can add to the Blue Lagoon tour swimming with stingrays or dophins, which would make it even more expensive, but unnessary. You can visit Stingray city there, and it was really crowded with people trying to snorket around. I don't think you could get to the Blue Lagoon on your own.
Last year, we went to the Hotel Atlantis in Nassau on our own. This place is a MUST SEE!!! The cruise line will offer tours from $50 and up. You can get there by water taxi at $6 per person both ways. You can walk around the hotel for free. To see the famous underwater aquarium is $25 per adult, however, the guards at the entrance are not very carefull and a lot of people I talked too actually sneaked in without paying. I hope that helps, Camelia