In St. Thomas, there is Meagans Bay, short taxi ride, about 20 minutes or so, beautiful beach, although no good snorkeling. If you want to spend more time, you can take a cab to the ferry and go over to St. Johns/Trunk Bay or a few other nice beaches there. Travel time to there is longer, but worth it if you want to snorkel.
In St. Kitts we took a 45 minute cab ride out to Turtle beach, beautiful scenic drive and a nice beach. You can see Nevis from there, restaurant is on the beach too. We had the driver just come back at a set time for the return trip.