I am an avid snorkeler (don't scuba dive). When I stayed in Cozumel in March 2005 (pre-Hurricane Wilma), the best place for shore snorkeling was definitely Dzul-Ha beach club, just a little to the north of the Fiesta Americana. There were big coralheads of lettuce coral that came up to near the surface in about 8-10 ft of water, and lots of fish were present. All the guidebooks and on-line sources mentioned that this was the best place, and they turned out to be true. I haven't been back since, but according to posts on this board and others that I have read, Dzul-Ha, similar to all shallow areas, got hammered pretty hard by the hurricane. Most of the coralheads were toppled over, but I've heard they still provide plenty of habitat for fish and other creatures. I suspect its still the best spot on Cozumel for shore snorkeling, although it will take a long time to become what it once was. Another plus for Dzul-Ha , as someone above mentioned, is that it is a fairly reasonable taxi fare from town. When I was there, there wasn't much beach, just a rock stairway to enter the water for snorkeling. There were shaded lounge chairs and a snack bar for lunches and drinks. I really liked the place and hopefully it's still open. Maybe someone who has been there recently will also reply to this post to give you an in-person update.
Hope this helps.