Our personal favorite is Pancho's Backyard. Service is great, food excellent, clean restrooms, safe water. It is located inside of the Los Cinco Soles shop.
We did Fat Tuesdays, the margaritas were great, don't remember much about the food Seriously though, the food was good. I've heard great reports about Poncho's as well.
Pancho's Backyard is a great place. I agree about Carlos 'n Charlies - great place to get a drink and stress test your hearing, but the food is not that good.
Pancho's is ok, but over-priced for Cozumel. If you want good food at reasonable prices, get a few blocks off of the coast. It's very safe to wander around town in Cozumel.
Some of our favorites: El Moro (by the airport), La Choza, El Capi Navigante, Costa Brava, La Mission. For El Moro, you need to take a taxi but it's definitely worth it.