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Without tourism, Cancun would be just another fishing village. They have plenty of options for transportation, no reason to rent a car. The whole place is a big hotel. Look at the signs in the Centro and pick one. If you don't like it, try another.2
I've stayed at a couple of decent hotels with parking in downtown Cancun (Hotel Tankah and Hotel Los Girasoles),but they're a bit below your price range, being around $35/night. Maybe try searching Tripadvisor?
