If you go south from Cozumel's principal town, San Miguel, you'll come to Chankanaab Nature Park, Playa Corona, Playa San Francisco, Playa del Sol, and the ruins of El Cedral. Farther south past Playa de Palancar -- the famous reef lies offshore -- is the island's end, where a dirt trail to Laguna Colombia leads from the Paradise Café. The road north is quite rough and only half of it is accessible by car. Walk north along the beach to Castillo Real, another Maya site. There are other minor ruins in the area, including Punta Molas Faro, at the island's northern tip. If you travel west on Avenida Benito Juárez, you'll come to the turnoff for the ruins of San Gervasio.
Cozumel is 33 miles long and 9 miles wide, but only a few of its roads -- primarily those in the southern half -- are paved. It's worth renting a vehicle to explore the island, which has more sights than either Cancún or Isla Mujeres. Most of the dirt roads are not maintained, so proceed with great caution, especially after a rain. Mopeds and motorcycles are very popular here, but also extremely dangerous because of heavy traffic, potholes, and hidden stop signs.