You can stand in line and rub shoulders with tourists and some locals at the hottest spots on trip advisor like El Chaya or Chaya Maya but the reports I've had from guests are that it's a 50/50 proposition. You'll love or hate it. I like the hand made tortillas and that's about it. The owner of these two restaurants also has a hacienda that has long been a destination for Sunday afternoon meals and events like weddings or 'quinceaneras". I've had one meal in 11 years at Hacienda Teya that I enjoyed.
My canteen when I moved here was the stand at the corner of Santiago market, El Reina de Itzlana
for paunches and tamales. The freshly made fruit shakes are great too. The open around 8 but it's really best to go around ten when the place fills up with locals. It's not open for lunch.
La Tradicion and Los Alemendros are popular with locals but that doesn't make them good. They both have locations in centro.
I get out of town pretty often for my Sunday bike rides and when guests are in town we get in the car and do the hacienda, cenote, ruin and church tour. Some of the best meals are at roadside stands like the goat beside the road in Motul or the grilled quail in Oxkutzcab. Constantly good are El Principe Tutul Xui in Mani and Kinich in Izamal. If I were going to one of the Starwood haciendas I almost surely order the Yucatecan dishes as chances are the chef has recently left and someone from the villages is filling in. I think the best dishes at Hacienda Xcanatun are also the local fare.
It's worth reading the reviews at Los Dos Cooking School before you head out on your own. Here is a link to his list of recipes...good to know what your in for.
I have been to El Chaya as of March 9, 2013 and I can promise you I will never go back it was absolutely revolting bordering on vomitus with a capitol V. Someday I will elaborate but for now the rotten lettuce and clamless clam shells in my overcooked fish dish are too fresh in my memory.... I've had tastier acid reflux.