I am a beach and nature person.
So, on our St. Thomas stop, we took the ferry to St. John and wanted to go snorkling at the National Park beach. But the current was bad, and the water was a little cloudy so the beach was closed for snorkling. We took and island tour instead. Maybe one day we'll get back for a few days.
At our Antigua stop, well, we weren't impressed with Antigua. The beaches near the cruise ship were just ok. We took a snorkle-sail trip around the island, stopping at a beach for barbeque and snorkling. It was just ok.
Barbados, we were there for a week on a timeshare exchange. We liked the beaches, and took and island tour that we liked. For a day, I'd recommend an island tour.
Haven't been to your other stops. Go on cruisecritic.com and read the forum boards for the ports your ship will stop at, for detailed info of what others have done.