On Cozumel the best hangout and bar is definately Carlos and Charlies but Senor Frogs is a neat place as well. Rent a car in Coz and drive around the island sightseeing and maybe stop at the small ruins, local taverns for a 'cold one', the Lagoon for a little beach thing and snorkeling, and also some nice shopping downtown, You could also opt for the tours like the jeep safari and horseback riding which are also great fun. In GC Stingray City is a must do and will be a lifetime memory. You can also snorkel free about 300' to the right of the tender docks at Edans Rock and the Devils Grotto, two of the nicest snorkeling spots I have every been to! Lots of coral, walls, fish, coral heads, etc.
Jim