There are some general rules when it comes to traditional Tenerife cuisine, like coastal areas are better for fish whereas inland towns and villages are the places to go for grilled meats and hearty stews. But some areas have quite specific foods linked to them.
Celebrating San Juan is a big thing on Tenerife, especially in places where traditions are strongest and reach back centuries. Its origins lie with the island’s aboriginal people...
Buenavista is another north western Tenerife town that stays off the tourist radar despite having some charming parts and a pretty town centre.
Wherever you are on Tenerife there's a good chance that there's a decent market not too far away and they're always worth a nosey. Here's Real Tenerife's complete (almost) guide to farmers' and agricultural markets on Tenerife.