Daypasses at any of the 3 Cable Beach hotels or the British Colonial Hilton.
Daypasses at Breezes for the partiers.
Many great places to see within walking distance of the pier.
Rawson Square, Paliament, The Queen's Staircase (my favorite), Fort Fincastle(awesome view of the island), Government House, Graycliff Cigar Factory, Piarates of Nassau Museum, Ardasra Gardens and Zoo.
Plenty of shopping les than a block from the Pier at either the Straw Market or all along Bay Street.
On Paradise Island you have Cabbage Beach, Atlantis Casino and Galleria (the pools and waterslides are off limits except to hotel guests at Atlantis or next door at Comfort Suites) and also the Digs Aquarium at Atlantis, which you can get admission at the Casino information booth for $29 per person. (or if your ship is in port late enough, like the Sensation was both times we went, you can get in free after the guards leave for the day after 6PM. Worth it for free. I wouldn't pay $29 to see it IMO)
Just a few ideas off the top of my head.
As you can tell, we LOVE Nassau.
Legend - Sept. 18, 2011 - Cozumel, Belize, Roatan, Grand Cayman
Fascination - Half Monn Cay, Nassau
Nov. 13, 2010 -
Sept. 18, 2010 -
Sept. 19, 2009 -
Inspiration - Jan. 10, 2010- Grand Cayman, Cozumel
Freedom - February 8th, 2009 - Key West, Grand Cayman, Ocho Rios Jamaica
Glory - September 8th, 2007 - Key West, Cozumel, Progresso, Nassau
Sensation - Freepor-Nassau
Jan. 28th, 2007 -
Sept. 10th, 2006 -