Here are a few suggestions:-
Palm Island in Aruba is a a great place to go if you like snorkeling its fabulous, take the day pass if you can as we only did the half day and wished we had done the full. Its very reasonably priced as well last December it cost $89 each for the day but this includes unlimited alcoholic and soft drinks and lunch, snorkel gear and instruction.
Bonaire - you can take a water taxi to Kliene Boniare a nature reserve again brilliant snorkeling here $10 per person return. Be prepared for a wait for the taxi though.
Grenada - you get hassled a lot here so if you are going to do anything, I would do a Princess tour.
Barbados - easy to get around. Cruise ship docks right by the town and easy to get taxi's and you would feel safe doing something on your own.
Antigua - ship docks right by the town, stroll the shops then get a taxi to one of its lovely beaches.
Tortola - take a taxi to Cane Garden Bay which is gorgeous or take a trip to Virgin Gorda which is absolutely beautiful.
Hope this help.
We are also going on the Sea Princess on 15th December This will be our 6th time in the Caribbean - a must do is the rum runner in grenada such fun and and experience not to be missed.
Hi we went on the sea princess 2 years ago at xmas time to the Caribbean and are going again this year and all i can say is use the local taxis or trips that are freely available on the dock side these are much cheaper and we found that the driver or guide new more than enough. also it is a good way to make acquaintances..see you their "in the sun.