I have been to Cozumel a number of times, and have rented a car and taken taxis. When we stayed in Cozumel we rented a car and toured the island, very easy to do, just remember to gas up before you return it. Higher gas prices than you will be used to but way better than what they charge when you turn the vehicle in NOT full.
But my favorite thing to do in Cozumel when stopping for a cruise is to taxi to Paradise Beach. Very nice beach, kept very clean, a nice young Canadien guy Tom runs the place. They have plenty of beach chairs, water sports for the kids, good food servd in the restauraunt, or at your beach chair (MY FAV).
The waiters are very attentive and easy to get a taxi back, and lockers are available. MY next favorite thing is the outdoor showers. To enjoy the beach all day, and then not feel allsticky for the ride back, and shopping in town is wonderful. I always bring some travel size shampoo and soap.
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