If you are looking for a great party atmosphere, head to Plaza Punta Langosta (Punta Langosta Pier). Just a 10-minute taxi drive from the main Cozumel international port, you can find here Carlos and Charlie's and Senor Frogs, which are the 2 places that compete for the rowdiest crowds. The food is a mix of Mexican and American pub fare, but the portions are very generous. There are daily drink and happy-hour specials throughout the whole day. Head 10 blocks northeast from these places to find Pancho's Backyard on Rafael E. Melgar 27 for some great traditional Mexican food.