Here are a couple of options for your Discover Scuba Diving Experience.
Underwater Safari's- They are right at Havensight where your cruise ship comes in and cater to people off the ships who want to try diving. You'll get a fun morning on the boat with some good diving, most likely on Buck Island. Ask for Zan if you go, he's a great instructor
Coki Beach- As mentioned earlier they will pick you up and drive you to the east end for a shore dive. The beach and reef of Coki is quite nice and can be a good way to try diving. Ask for Chris (not me) or Harley good instructors!
Chris Sawyer Dive Club. Also on the east end, you can make your way over for a morning dive on their comfortable boat. Most likely diving off the North side of St. Thomas or one of the cayes (Grass or Mingo) to the north. They are a well known (on St. Thomas for over 20 years) operation and you'll have a great time with them. Ask for Tricia, she's a great instructor
Last but not least is Blue Island Divers in Crown Bay Marina. They just got a new boat which is fast and comfortable, a classy operation. Ian can take care of you there!
Enjoy,
Chris