There is only one city on Cozumel, and it's called San Miguel. The downtown and main square is a beautiful area with lovely shops for jewelry, T-shirts and exciting Mexican and Mayan decorations and souvenirs. There are also a number of great restaurants downtown, plus banks and ATM machines, pharmacies and a local market with handicrafts, leather and silver. Be sure to visit the square Sunday evening where there is fun, fiestas and music to enjoy.
Taxis are very plentiful, and quite reasonably priced and rental vehicles are available.
Looking toward the water from Ave. This is the main waterfront street has a beautiful view of the ocean. The street is lined with shops of all kinds and there are several very striking monuments, including the Mayan statues and the divers arch. Right across from the main square is the dock where you can catch a ferry to the mainland. The trip takes just under and hour, and the ferry takes you to Playa del Carmen.