Welcome and congrats on your upcoming first cruise!
Since you mentioned snorkeling i will highly suggest that you take the time and make the small effort to get your family over to St. John Island when you are port at St. Thomas. Getting a taxi is really easy at St.Thomas, there are taxi vans lined up at the pier and people to guide you to your taxis. It takes a taxi trip, a water ferry ride and a taxi to the beach on St. John, go to www.vinow.com
for great info on the water taxi, and beaches. St. John is a gorgeous island and the snorkeling is very good. If you feel uncomfortable doing this on your own then by all means book a ships tour to St. John Island. If you want to stay on St. Thomas proper then i would suggest Sapphire Beach. Do your beach in the morning, go back to the ship, drop off your beach stuff, grab a bite to eat and then go shopping.
St. Maarten is another gorgeous beach island, again taxis are very easily available at the pier. Orient Beach is by far the most popular beach on St. Maarten, it is a french beach so it is topless and there is one section way down the end that is clothing optional. Dawn Beach is another great beach choice. We booked a ships excursion on our last trip to St. Maarten we booked the Golden Eagle Catamaran sail - totally loved this excursion, and would do it again in a heartbeat. Its a great family trip. You sail on this beautiful cat over to Tintimar island preserve where you can swim, snorkel, veg out on the beach, food and drink is provided.
Definately bring your own snorkel and mask, rent fins.