I just came back from that cruise. You will love it!
In St. Thomas we just took a taxi to the beach. It was gorgeous. But I've heard Paradise Point/Coki Beach/etc. are all great too.
In Dominica I did the Dominica's Favorites through the ship, which was well worth it. It went to Trafalgar Falls and Emerald Pool and I saw a lot of the rainforest. The aerial tram is probably awesome as the rainforest is absolutely gorgeous.
Went snorkeling in Barbados through a Carnival excursion.
In Antigua, again we just went to the beach via taxi. It was much cheaper than going through the ship and it was paradise defined.
I was disappointed I didn't get to see the island in St. Kitts. We woke up too late... But friends of ours found a Party Bus at the end of the pier (there are a bunch of locals that have booths there) and for $15 pp they were taken all over the island, to the beach, and had all the free rum punch they could drink. They loved it and said it was the best island we had visited.
Anywhere you go, sometimes you can get an awesome deal with a local company right inside the main pier area. Be careful on your time though-you don't want to miss the ship!
I hope you have a great time. This was probably the best vacation I've ever taken!