I'll try again.. my last reply disappeared...
Last time we headed to Nassau we went to the Blue Lagoon. Its a nice beach day away from the city. You can buy tickets on their website. You don't need to go through the cruise line (although you can save the cost of the taxi ride to the Blue Lagoon ferry terminal if you book through the cruiseline)
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013