We did a little geocaching on the island as well, which was fun.
We went to Palancar beach, which I can't really recommend. The food and drinks were good and reasonable, but the facilities were not so much. It is further out than the other beaches, so the cab ride cost twice as much. The beach area itself was very narrow and steeply sloped. The lounge chairs sat at about 45 degrees. They were not crowded at all, so we put our things around a table in the outside dining area. While we were getting situated with swimsuits the waiter came by and curtly reminded me that the tables were for food only. I politely gathered all and moved it to the sand and ordered some drinks and guacamole (delicious, and came with great homemade chips and salsa as well.) I had packed some sandwiches for our finicky kids, and was quickly chastised by the waiter that no outside food was allowed. I hear the snorkeling there is very good, and I saw a few people braving the chilly water. They took a cute picture of us in sombreros as we came in, and asked for around $12 for the print later. They have a reasonable gift hut at the entrance. Bathrooms were needing some repair (a toilet seat missing in the ladies') and the outdoor showers weren't heated (it was not a warm day) but the changing rooms were generously sized.
Last time we went to Cozumel we went to Chankanaab in a cab and liked it much more. There was a much larger beach/sunning area and the snorkeling was great. You can get coupons online before you leave on your cruise, but it is on the pricy side for admission. Next time we'll probably try a different beach club.