I have been reading good things about Great Bay in St. Maarten on this board; it sounds like it is easy to get to. When we were in St. Maarten with our DS who was 2-1/2 at the time, we went to Dawn Beach and it was very nice. It was a nice family beach. There is a restaurant there, you could rent chairs and if I remember right, they had wait staff coming around to chairs on the beach taking drink orders (the special was Carib beers for $1). There were gentle waves at this beach which DS loved. It was a very scenic beach and there were people snorkeling out a little from the shore.
At St. Thomas, Megans Bay is a good family choice. They do charge a small admission. It is a public park and there are facilities and a snack bar. Another nice place to go is to Coki Beach which is right next to Coral World. The kids often enjoy Coral World and can enjoy beach time too.
I have read great things about Sappire Beach which is on the east end of the island. That is where I would like to go the next time we are in St. Thomas.
Also, as I mentioned on the other post, there is Morningstar Beach which may be the closest beach to the pier. It is a beautiful beach and there is a restaurant/bar right on the sand and bathrooms. If you want a short ride in the taxi, this is a good choice.
St. John is a beautiful island as well. I have been to Trunk Bay and enjoyed the underwater snorkel trail and the beautiful beach. I have had good and not so good experience (water was rough that time) with the ferry boat over to the island and have not been adventerous enough to try this yet with our son. Depending on how patient your kids are, this does take more travel time to and from but it is a gorgeours beach.
Decisions, decisions... so many choices, not enough time!!