Yucatan cuisine is well known throughout Mexico. Try the traditional "Pollo Pibil" tender chicken and "Sopa de Lima" chicken soup with lime juice. "Poc chuc" is a tender slow cooked pork dish. Chilmole is turkey in a dark spicy sauce. Venison is no longer so common in Yucatan as it was a generation ago, but still sometimes appears on menus and is usually of good quality.
If you are lucky enough to be discovering Yucatan by automobile or even bus, a travel cooler of decent size comes in very handy in this climate. You will have opportunities to purchase fresh fruit and vegetables along the road. Pass up any that have already been peeled. Honey is usually found for sale along the road in used whiskey bottles. It should be considered safe and surely will be quite tasty.