I went to a beach called.. Nachhio or something.. I can't really remember, wasn't really paying attention. NOt many people know about it. its about a 15$ cab ride from the ship, but it was really quiet, gorgeous white sand. I spent the day floating on my back in the ocean.. listening to the sounds of the water. Ask the cab driver in Cozumel. Its not NACHO beach..its like..nachhi or Nachhio.
clearly i'm not much help here..sorry!