If you are interested in getting in touch with native canarian people you should visit the nothern coast of the island.
In Arucas they are distilling original canarian rum. You should have a shot at this. It’s delicous!
The most spectacular one, I think, is the “Cueva Pintada” placed in Gáldar. You will discover cave-paintings in white, red and black colour.
The biggest cave you will see in Tunte (San Bartolomé de Tirajana), which has been the aboriginals living room and granary.