Alot depends upon what you want to see and do.
Nassau - definatley take the group over to Paradise Island to Atlantis Resort - take the tour of the aquarium/dig. It is fasinating. The cost is $25.00 per person but worth every penny. Just grab a taxi - either water or land at the pier.
St. Thomas - hit the beaches, do some snorkeling, do some shopping, hire a local for an island tour. My top pick for a beach on St. Thomas proper would be Sapphire Beach - beautiful with good snorkeling. Meagan's Bay Beach is the most popular - but it gets very crowded,touristy and there is no snorkeling there. If you want to take the time and make an effort- take the ferry over to St. John Island - it is beautiful- beautiful beaches with great snorkeling. - check out this link- www.vinow.com
. Trunk Bay is the most popular - there again gets very crowded with all the cruise ship passengers.- do it on your own, don't book a ships tour- a ships tour to St. John really limits your beach time.
Try to budget about an hour at the end of your day to take the Paradise Point Tramway - its a short walk from the pier, the view of the harbor from the summit is breathaking. You can shop at either Havensight Mall at the pier or in downtown Charlotte Amalie - we prefer downtown -more choices and more local vendors.
St. Maarten - beautiful beaches, snorkeling, shopping. You can hire a cab for a few hours to take an island tour.
One of our favorite things to do in St. Maarten is the Golden Eagle Catamaran sail - you can only book this thru the cruise line. Its a great tour for all ages, you sail on this beautiful cat - sail up the coast which is gorgeous, you sail over to a small island where you can swim, snorkel, relax on the beach, or just go for a walk. The boat provides lunch and drinks(alcohol & non).
If you just want some beach time then head over to Orient Bay Beach by taxi - this is a great beach - one section is clothing optional - it is clearly marked and at the end of the beach. Being that Orient Bay is on the french side of the island it is a topless beach. Looking for something more family friendly then head over to Dawn Beach.
If you want to do some shopping you have two choices- the french or dutch sides of the island. The french side has more "high-end" designer items as opposed to the Dutch side which i think has better jewlery, linen, fragrance and cosmetic bargains- better than St. Thomas -imo.
Hope this helped and didn't confuse. A great place to start looking is at the ships excursions, this will give you a general idea of whats available.
Then you should check out Frommers or Fodor's travel guides - either online or at the library - they are full of great information.