In "real" Cancun, vs. tourist Cancun, there are some great restaurants, including the legendary La Habichuela and, nearby (and with the same owners) Labná, which focuses entirely on traditional Yucatecan/Mayan cuisine.
I actually found a private guide who picked a friend and me up in Cancun and drove us across the peninsula. We visited Chichen Itza, spent the night in Vallodalid (famous for its sausage), visited Celestun Bioreserve (where all the flamingos winter), toured a sisal plantation and climbed down into cenotes, deep caves with underground lakes and rivers, and ended up in Merida, where we spent a few more days, exploring. (So I agree with Diannie that it's a good destination.) If you go to Merida, definitely dine at Restaurant Los Almendros -- the place locals will send you for authentic Yucatecan (which is not much like other Mexican food). The service was wonderful, especially when they discovered that I was really interested in the local specialties. Must tries of the local specialties include stuffed cheese and venison soup, plus salbutes, panuchos and papadzules, cochinita pibil, and poc chuc.
Because few Americans visit Merida, even the breakfast buffet in the hotel was a thing of beauty.
I'd recommend a bit of a wander about the Yucatan, if you can manage it.