La Chaya Maya is the restaurant most reliably recommended for traditional Yucatecan food, and the recommendations are warranted. The menu covers the full range of regional cooking: cochinita pibil (slow-roasted pork marinated in achiote and sour orange, cooked in a pit), poc chuc (grilled pork in citrus), sopa de lima, papadzules, and several dishes less commonly found elsewhere, including the egg-yolk–based egg dishes that form part of the Yucatecan canon. The chaya juice drinks — chaya being a leafy green native to the peninsula — are genuinely good and worth trying.
The restaurant has two locations near the centre, both on Calle 62; the original is a few blocks north of the Plaza Mayor. Prices are mid-range by Mérida standards, which means very reasonable by any international comparison. The Sunday Yucatecan buffet is excellent value and a practical way to sample a wide range of dishes if you are new to the cuisine. Lunch is the main meal here; the place is busy from noon onwards and it is worth arriving before 1pm to get a table without waiting.