Hi Heather, and welcome aboard!
Won't it be nice to be heading for the warm waters of the Caribbean this November? I bet you're really excited!
If you're looking for a nice beach close to the port in St. Thomas, I've heard great things about Morningstar Beach. It's not a far taxi ride from the port, and is located near the Marriott. You don't need to be hotel guests to enjoy the beach, but they do charge a fee to use the beach chairs and umbrellas. You'll also find several bars and restaurants right there.
In St. John, I'd recommend Trunk Bay. One of
Disney's Port Adventures takes you there, but you could also access it on your own. It will require a bit more planning though. You'll need to take a taxi to get to the ferry dock from St. Thomas to St. John. Once in St. John, you can take another taxi to Trunk Bay. Just watch your time, because you might have to wait a bit for the ferry. Taxis are pretty readily available, so that part shouldn't be a problem.
Have a great time on your cruise and as you explore the islands, Heather!