Rent a car and drive out of Cancun. It's a weird place, and not like the rest of Mexico at all. In fact, the first time I went (for work) I came in from Merida, and it felt like I had flown back to the States - except they spoke less Spanish.

You can either go down the coast towards Playa del Carmen and Tulum - but it is still full of resort hotels. We had a wedding there a couple of years ago, and after the wedding escaped, and drove via a visit to Chichen Itza to the Hacienda San Jose - about 30 minutes outside Merida. That was a pretty amazing hotel - and there are several more of these unusual hotels in the area - but obviously no beach.