The Havensight Mall at the pier is where we do any shopping we might want to do. As Jim said, the same stores are at Havensight as there are downtown. It is easier since you are literally just a few steps from the ship (well, maybe a football field away).
However, if you go downtown to the main shopping area in Charlotte Amalie it is quite safe, as are the drivers and taxis. This is the well-beaten path. Just make sure you are clear on the price before getting in the cab. Also note that traffic in the Virgin Islands drives on the left side and it is very congested so be careful crossing streets.