Take my advice and visit a couple of the bigger cities in Yucatan - like Merida and Valladolid. You can skip Cancun, because I think it has lost its charm of a typical Mexican town. In Merida or Valladolid although you can see the growing influence of touristic development, there are still more than a handful of historical buildings around and as you wander the small streets, quaint little shops, authentic restaurants and tapas bars can still be found. Try to start exploring the surroundings areas from the city center.

I like to visit the smaller towns in the rural areas. Here you can see much better the authentic style of living in Yucatan. There is not a lot of rural development and most buildings are not well maintained. Nonetheless, you will find colorful houses, very pretty gardens and patios.
On my vacation in Yucatan I preferred to stay in bed and breakfast lodges that are privately owned. Most of them are in quiet areas and very guest friendly and offered a good sumptuous breakfast. If you are lucky, some of them would offer a shot of Tequila as a welcome gesture.

Here are my recommendations for places to stay:
The Pickled Onion in Santa Elena near Uxmal - cute bungalows, a fruity breakfast and locally-made honey.
Posada Yum Kin in Tulum - you might miss a little bit of privacy here (my room was on the ground floor), but super nice patio.
Luz En Yucatan in Merida - near the city center but quiet and free Tequila by the reception, only drawback the rooms have no sunlight.
Hotel Oka'an - close to Ik'Kil Cenote & Chichén Itzá and located in the middle of the tropical jungle - quit and very nice staff. You can see the tip of El Castillo from the top terrace.
Hacienda San Miguel on Cozumel - the charm of an old Hacienda. The owner and staff are locals and very friendly and helpful.