Alexok,
Welcome to cruising and to these boards!
For your first visit to St Thomas I wouldn't try to do too much. You'll just end up doing many things half way. Instead, choose what you would most like to do and devote the day to it. The shopping in St Thomas is about the best in the Caribbean, so if that is appealing to you this is the port to save your energy, time, and money for. There are many shops right at the port, but more downtown (a five minute cab ride away). And, downtown has some additional charm with its narrow streets, back alley shops, and second floor lofts. The dock-side shopping is more like a US strip mall. Nice selections, etc but not charming in any way.
If you prefer beaches, by all means go to St John. There is nothing like it elsewhere. Ninety percent of the island is now unihabited, and is returning to nature. Trunk Bay and several others are gorgeous spots where you can swim, snorkle, sun bathe and forget the stresses of the real world. There are some nice beaches on St Thomas itself, but they will be crowded and, at least in my opinion, do not come close to their counterparts on St John for knock-out beauty. You can get to St John by taking a cab to Red Hook and then taking the ferry. Once there, you can either rent a jeep for the day and scout out the island on your own (there really isn't but one road -- you can't get lost), or you can hitch a ride on one of the open air touring "buses". Or, if that is a little intimidating for a first timer, your cruise ship will probably offer an excursion that gets you there and back. Either way, St Johns is the tops if you want a beach day.
Enjoy your cruise and welcome again.
Ted