We were in St Thomas last March on a Sunday. It was one of the best port days we ever had.
We were on the Serenade and the only ship in port. WE walked off the ship, into town and then up to Blackbeards castle. We then walked into the shopping district and found... no one, the stores were all open for business but the streets were almost empty. We have always been in St Thomas with at least 3 other ships and it is very busy and this was a very nice change.
As Dave noted Havensight was open for business and also very quiet.
You will have a great time, enjoy.