Nassau - you and your teens would love touring the Aquarium at Atlantis Resort. Its an amazing place. Very easy to get to, just grab a cab(either land or water) over to Paradise Island and Atlantis Resort .
St. Thomas - the best beaches and snorkeling here is over on St. John Island (IMHO), again very easy to get to, grab a cab at the pier, head to Red Hook Harbor, buy your round-trip ferry ticket over to St. John Island, once you dock in Cruz Bay grab a cab-the open air jitney's to any of the the beaches -go to this web site for valuable information- www.usvinow.com
. Beach in the am, come back to the ship, drop -off beach stuff, grab a bite to eat then head out to shop - you can shop either at the mall at the dockes (Havensight Mall) or you can grab a cab into downtown Charlotte Amalie, most of the same shops in both locations, but downtown has more small souvenior, crafty, and touristy stuff.
St. Maarten - if you want a really neat snorkel adventure then book ships tour over to Pineal Island. If you want to just hit the beach then Orient Beach would be the place to go, this is on the french side so the beach is topless, and there is a totally clothing optional section at the far end of the beach - clearly marked.
Another really cool excursion in St. Maarten is the Golden Eagle Catamaran Sail - we had a blast! you sail up the cost (gorgeous) over to this little island preserve (Tintamar) where you can swim, snorkel, lounge on the beach, food and beverage is provided.
As for shopping for jewelry - both St. Maarten and St. Thomas are very good ports, attend the ships shopping lectures, know your prices before you leave home, be an informed consumer. St. Maarten is much more laid-back when it comes to sales pressure than St. Thomas.