If you just want to hang on the beach, there's a free beach next to the Atlantis in Nassau called Cabbage Beach. I don't remember seeing snorkel gear rental, I had my own. However, there was no good snorkeling there. Grand Turk there's a beach right where you dock with chairs and a shopping area. The snorkel trip we took was through the ship and we had 2 very nice stops. One was for great coral the other was great fish, including a huge barracuda.
As Dave stated, Half Moon Cay is a private island. Hope this helps.