This 2,700-acre park, formerly called “Punta Sur,” is a 30-minute drive from the traffic of San Miguel, Cozumel’s main town. The refuge contains secluded beaches — only some of which are safe for swimming because of currents — snorkeling sites, mangrove lagoons, shrub thickets and wind-blown dunes. To explore the park, board one of the trams that bump along, past dense thickets of sea grapes and palm trees, to the 19th century Celarain lighthouse. The reward for climbing 133 stairs is a panoramic view. You can also kayak or go on a catamaran sailing through the Colombia lagoon. Since the park is situated at the tip of the island, it’s generally less expensive to rent a car in downtown Cozumel than it is to take taxis, which may be scarce when you wish to return.