Hi if you put this question in body and soul there is a member on there at the moment called legend who lives in los christianas in tenerife I am sure he would know
Masca (in the NW of the island) was a good example but since the decent road was put in there it gets overrun by visitors, as always happens.
The parts of the island that retain the most Canarian culture are (unsurprisingly) in the areas tourists don't often go to. Hire a car and go up to the far NE of the island and you see what I mean.