I would highly recommend Admiralty Dive Center on St. Thomas. Smal charters, very personalized service, owners and staff are the best, tons of dive site variety, sites selected based on experience of divers as well as weather/sea conditions. They will pick you up at the cruise ship dock. (OK, I am a bit biased since the owners are two of my best friends, but they are also the ones who instructed and certified me, and they are genuinely good people who will work with you to make sure you have an awesome experience.
Admiralty Dive Center