In St. Thomas there will be lots of locals at the port ready to take you to the downtown shopping area for a few dollars. If you go on your own you can visit whatever stores you want and not just those 'suggested' by the cruise company.
There is also a large shopping center right at the cruise dock so you can also go to the beach on your own, then leave in plenty of time to get back to the ship and then shop up to boarding time.
On our last St. Thomas stop in March we enjoyed a great time at Trunk Bay on St. Johns Island. We got there on our own using the locals to get us to the ferry and to the beach. We spent more time at the beach then we would have had we taken the ship's tour.
February 1998 - HAL Westerdam E. Caribbean
January 2000 - Carnival Ecstasy - Mexican Riviera
February 2002 - Costa Atlantica - W. Caribbean
February 2004 - Grand Princess - W. Caribbean
March 2007 - RCI Voyager of the Seas - E. Caribbean
May 2007 - RCI Voyager of the Seas - Western Mediterranean (Mrs. E. & daughter only - I had a medical emergency)
October 2007 - RCI Adventure of the Seas - Southern Caribbean