St. Thomas - you can just grab a cab at the pier, hire the driver for a few hours to just tour the island. A short walk from the pier is the Paradise Point tramway-its about a 7 minute ride in the tram up to a beautiful overlook. There are lots of things to do and see at the summit-- shops, restaurants, botanical garden - go to their web site, same as their name. If you just want to shop you can do that at either Havensight Mall at the pier or grab a cab into downtown Charlotte-Amalie.
St. Maarten -grab the water ferry(Dutch Side) into downtown, wander around, do some shopping, stop at the Guavaberry Emporium for a sample of the local liquer. Grab a cab at the pier and head over to the French side - do some shopping and sightseeing.