The ship (the Captain doesn't like it when you call it a boat) docks at Great Bay in Philipsburg. Great Bay beach is large and convenient to both the ship (via the aforementioned water taxi) and the downtown shopping area. The only thing that I don't like it for is snorkeling. There's a lot of watercraft in the bay and it seems a bit cloudy. It's great to swim or rent a jet ski, though. Don't get me wrong, it's still a great blue color, but just seems as if there's a bit more sand kicked up in Great Bay than at other beaches.
Little Bay beach is just west of Great Bay, probably only a 5 min cab ride. That might be convenient for your plans, too.
If you want to snorkel, I'd recommend Dawn Beach. It's about a 10-15 minute cab ride from the cruise ship pier. There's a restaurant there with restrooms, and you can rent chairs umbrella, floats, etc. right there. The water will be warm wherever you go. We were last there in December and even though it was raining in the morning, we stayed in the water at Dawn Beach until we were too tired to swim any longer. We never got cold.