St. Maarten and St. Thomas are your best shopping islands. The best deals will be on jewlery, liquor, linens, perfumes, small electronics (camera's). We found the shopping in St. Maarten to be better than St. Thomas. Both of these islands have goregeous beaches. There are a couple of really fun excursions to do on St. Maarten - the Golden Eagle Catamaran Out Sail - you sail up the coast which is beautiful over to this small island natural preserve where you can swim, lay on the beach or go snorkeling. Book the tour in the am so that gives you time to go into town in the afternoon. Also the America's Cup Regatta is a total blast! you get sail and actual cup sail boat in an actual race. If you just want to hit the beaches in St. Maarten - grab a cab to Orient Bay - the most popular -there is a clothing optional section of this beach. Dawn Beach is another great beach on St. Maarten- more of a family beach. If you want to snorkel in St. Maarten look into a tour over to Pineal Island.
St. Thomas - do it on your own. Beautiful beaches - especially over on St. John Island which is just a water taxi ride over from St. Thomas. Good snorkeling also. Many beaches to choose from. Trunk Bay is the most popular- it can get crowded. There are lots of other great beaches to choose from. Do the beach in the morning and then you could do some shopping or grab a cab for a couple of hours and tour St. Thomas - make sure you go up to the top of the island for a great scenic view .
Go to Princess web site and click on shore excursions to get a good idea of what to do.