If you have a day, waterlemon is a great snorkle spot. You have about a mile and a half hike. Salt Pond Bay is also a good spot that isnt as busy. There is about a mile hike. Anything less crowded will be a hiking beach.
I dont know about St Maarten.

I doubt the Disney ship stops in St. John; it probably docks in St. Thomas (unless you are on an unusual trip for that ship). If so, you should keep in mind that there might not be time for Chris' suggestion (which is otherwise sound).

The cruise ship docks in St. Thomas are AT LEAST a 1/2 hour taxi drive to Red Hook. From Red Hook, you would take an every-hour-on-the-hour ferry to St. John, and that trip is another 1/2 hour. A taxi to the Anneberg Ruins on St. John (from where you can hike to Waterlemon) is going to take at least 20 mins; Salt Pond is double the distance. Make all of this round-trip and double the taxi / ferry fares, and you are spending most of your day paying people to move you around, rather than looking at the undersea life.

If Disney is in St. Thomas instead of St. John, you have a few equally attractive options. You could take the excursions arranged by the ship. There are probably snorkel excursions by taxi to Coki Beach, which has very nice undersea life. There probably also are excursions by sailboat to Buck Island, which usually includes a snorkel stop. The snorkeling there is good. If you want to avoid the ship's offerings and go by taxi, I would recommend Sapphire and Secret Harbor, two resorts with decent beaches and good snorkeling from shore. None of this snorkeling is as good as you would get on St. John; but that doesn't matter if you don't have time to visit St. John. Also, all of these snorkeling spots are likely better than anything you will find in St. Maarten.

Enjoy your trip!

Doesn't Sapphire "host" and have an arrangement for the Dizzy Ship to use their beach the day they are in port on St. Thomas?

PS. Sorry to have missed you AGAIN!

I agree that Chris' suggestion of Waterlemon is a good one... however MsChuy is correct as a cruise passenger calling on St. Thomas you will spend about 3 hours getting to and from Waterlemon, taxi to dock, ferry ride, taxi to trail, hike... then all that in reverse. The ferry ride and taxi ride is fairly scenic... so if you don't mind the commute then cosider this still an option... if you would rather spend more time on the beach then go to one of the beaches closer to Cruz bay which will be busier because they are easier to get to and also because many tours go there - and those would be Trunk Bay, Cinnamon Bay... Hawksnest is lovely also.

--Islander