Because most of the cruise ships offer Playa Sol packages, it tends to be very crowded. If you'd like something with less people, you could try Mr. Sancho's or Nachicocom. They are both beach clubs in the same general location, but don't charge to enter. Nachicocom has a larger pool than Mr. Sancho's. If you decide not to buy the package through the cruise ship, you can catch a cab to one of the other beach clubs and go on your own.
You can also rent a car for about $45.00 (VW) and go wherever you want for the day.
Our most beautiful beaches are on the east side of the island, which is uninhabited, with white sand beaches and open sea. There are about five or six palapa type restaurants along that side of the island, where you can pull in and have a bite and something to drink.
Check out the cozumelinsider.com beach chart and consider renting a car and doing the island on your own. It's easy and you will discover the real Cozumel.
Ross in Cozumel