Cozumel is my favorite place on this planet and I am about to go there for the 12th time next week on a Carnival cruise. Hands down, I recommend getting a car, driving around the island and eating lunch at Mezcalitos (you can google it). It is a hole in the wall at the turning point where the road that circles the island meets the road that cuts straight across the island. It is right next to a little store selling blankets, etc.... it's 5000 shades of yumminess and peace and quiet. They have the BEST shrimp fajitas I have ever tasted and their guacamole is to die for.
Just a warning, they have outdoor plumbing and a white blue eyed cat (who loves shrimp) and sometimes a mangy dog hanging around but I've eaten there about 6 times (one my my favorite stops on the island) and have never gotten sick. The clean white sand beach and hammocks becon me on Tuesday....I'll be there for lunch as I am forgoing all of the "tours" to rent a jeep and take my friends on an island tour with Mescalitos being the featured stop.