So you want to know which is the best beach on St. Thomas and on St. Maarten? Wow, that is a tough one to answer. I am sure that you will get a little piece of everyone's opinion, and I guess I will go ahead and offer mine.
St. Maarten -- There are numerous choices, all of which are simply beautiful. I have personally been to Pinel Island to a private beach club which was beautiful and also to Mullet Bay Beach which was also very beautiful. Both were a little smaller and very quiet. If you have ever seen any of the videos floating around the internet of the huge planes landing right over a beach, that is Maho Beach and it is also beautiful, but you will occasionally have planes landing directly over the top of you there. Several of the catamaran snorkel tours will take you snorkeling and then stop at a beach as well. Of course, if you are really adventurous, you can go to Orient Bay Beach which is on the French side of the island and is officially topless. I have personally never been there.
St. Thomas -- In my opinion, and I'm sure Penny will second this, the best beach to go to is called Trunk Bay and it is located on St. John. You have to take a taxi to a town called Red Hook followed by a ferry boat to St. John and then another taxi to the beach. I know it sounds complicated, especially for a first time cruiser, but it is really easy and there will be lots of other folks doing the same thing. It is truly one of the most beautiful places on the planet! There is also an underwater snorkel tour that you can take on your own that is awesome. You can rent snorkel equipment right there on the beach for $5. As far as staying on St. Thomas, the most highly recommended beach is called Magen's Bay and it is also quite beautiful. You can simply get off of the ship at the terminal and ask for a taxi to take you there. It is simpler to get there than Trunk Bay and it is also very very nice. Either choice would be great.
Well, I hope this helps. I am sure that some of the more experienced folks will give you even more information, but since these are two of my favorite places, I wanted to chime in.