Hi and welcome to cruise-chat!
First, let me suggest you check out our sistersite PortReviews.com . Here is the link to the Caribbean Poprt Reviews: http://www.caribbeanportreviews.com
(just use the left hand navigational bar to redirect you to your specific ports).
But, since water activities are out - here are some suggestions:
Nassau - tour the "The Dig" (a very nice aquarium at Atlantis on Paradise Island), take a walking tour of Nassau or a horse-drawn carriage tour, visit Ardastra Gardens (a unique botanical garden).
St. Thomas - take the Paradise Point Tramway right across from the Havensight Mall, visit Coral World and shopping, shopping, shopping.
St. Maarten - take a trip by taxi to the French side of Marigot, visit the Butterfly Farm or spend some money in one of the casinos on the Dutch side.