If you don't want to take the ferry over to St. John, do your shopping right at the port (Havensight Mall), then take a local shuttle to Sapphire Beach for an excellent day at the beach. If you wish to add a bit of sightseeing into the mix - take the short cable car ride on the Paradise Point Tramway, across the street from the Havensight Pier. It provides a great view of the harbor, 700 ft. below.
If you go to Sapphire Beach, which is pretty, be aware there are a lot of small rocks when trying to enter the water. The north end of the beach has less rocks, and the snorkeling is good there as well, if the wind isn't blowing too hard. A cab ride to Sapphire is $11/pp each way.
The cab ride fares on St. thomas are very expensive. That PP charge of $11 is terrible. Sometimes it is less expensive just to do the ship excursion to where you wish to go and have the added benifit of being on a tour!
I have heard from other people who took the public busses there, they said you can go around the whole island for $1, somebody verify this if you have experience with it. The first time we went there we rented a jeep which was a lot of fun. We went to Magens and Morningstar Beaches and drove around to see the island, had a great time, though I prefer the Trunk Bay (St. John) excursion and the Catamran to St. John better.
DSR - One thing I make sure I do when in St. Thomas is go to the Tropical Deli. It is one block off the park where most people are dropped off by taxi. It has the best local food. Totally lacking in atmosphere, but the food couldn't be better. I always get a fresh Cuban Sandwich - have them wrap it and take it with me sight seeing.
Just a suggestions.
Hope this helps