So much to do in St. Thomas, you could spend a month there and not see all the nice beaches.
An easy do it yourself beach is on Water Island. The ferry to water island is an easy walk from where Royal and Celebrity ships dock. Dinghy's beach bar, on water island, has excellent food and drinks and wonderful beach. I've been to Coki beach at least four times, it has a local vibe, the snorkeling is really good, it can get a bit crowded, but that is part of the vibe. Coki beach is on the opposite end of the ports, so plan a good hour on travel each way.