the first place to start is on Carnival's web site, browse thru the excursions that they offer and see if anything interests you.
A lot depends upon what you want to do and see.
some General Ideas:
Nassau - go to Atlantis Resort and take a tour of the "Dig" its an amazing aquarium - just grab a cab(land or water) at the pier. IF you want some beach time in Nassau book a ships excursion to the Blue Lagoon- there are different packages offered at different prices. You can take a tour of the Pirate Musuem, walk around Government Center, go to the Straw Marketplace, visit the zoo.
St. Thomas - pretty much all about beaches, snorkeling and shopping. There are many beautiful beaches to choose from, go to www.vinow.com
for some really good information. You can hire a taxi for a few hours to tour the island. You can do St. Thomas very easily on your own. Shopping - two main shopping districts - at the pier - Havensight Mall or downton Charlotte-Amalie.
St. Maarten - another beautiful beach and shopping dream island.
look into taking the Golden Eagle Catamaran tour- thru the ship - its great - you get to sail, swim, snorkel, hang out on the beach, and have a bit of a party. Take the morning tour - this gives you enough time to get back to the ship, change clothes, grab a bite to eat and then head into town to shop - take the water taxi on the Dutch Side, or grab a cab and head over to the French side of the island to shop. IF you just want to hit the beach Orient is the most popular.