The island offers a number of good restaurants. Taxi drivers will often steer you toward restaurants that pay them commissions; don't heed their advice.
Zermatt (tel. 987/872-1384), a nice little bakery, is on Avenida 5 at Calle 4 Norte. Le Chef (tel. 987/876-3437), at Avenida 5 and Calle 5 Sur, is a deli/gourmet food store. It has a daily menu of salads, pizzas, and prepared foods, as well as cold meats, cheeses, baguettes, and other makings for a picnic. For inexpensive local fare during the day, I like Comida Casera Toñita (tel. 987/872-0401), at Calle Rosado Salas 265 between avenidas 10 and 15. It closes at 6pm. For morning tacos de cochinita pibil (traditionally a breakfast item), go to El Amigo Mario (tel. 987/872-0742) on Calle 5 Sur, between Francisco Mújica and Avenida 35. The owners close at half-past noon.
Finally, there's a new restaurant in town called The Wynston (tel. 987/869-1517). Albert Domínguez, the owner of Prima, brought a chef down from New York to run his new place at El Cantil condos. It was close to opening when I was last in Cozumel. I've heard the food described as Mediterranean fusion.