St. Thomas you can definately do on your own, if you are a beach/snorkel person and want to experience gorgeous beaches with really good snorkeling then you should think about getting over to St. John Island-you would need to grab a taxi at the pier head over to Red Hook Harbor, grab the ferry to Cruz Bay and then grab a cab to the beach, go to www.vinow.com
for ferry & beach info. If thats not quite your cup of tea and you just want to beach it i would suggest Sapphire Beach on St. Thomas proper, again just grab a cab at the pier, go to the beach in the morning and then do your shopping in the afternoon. IF you dock at Havensight the mall is right there, if you want something with a bit more local flair for shopping then you would have to shop downtown Charlotte-Amalie. Its all about budgeting your time.
St. Maarten - again a great beach island, the happening beach is Orient Bay beach- its french so its topless and there is a no clothing optional section, great beach, lots to do. There are a couple of great ships tours to consider on St. Maarten - Golden Eagle Catamaran Sail and the America's Cup Regatta, both top notch. Shopping on the dutch side of the island is easy, you walk the pier to the water taxi its cheap and it takes you right into downtown, if you want to shop the french side then you would have to grab a taxi