The only problem is that most of the Tenerife resorts are in the south and predominantly in either very commercialised areas or remote from everything meaning a car is essential rather than optional.
The one exception would be Puerto de la Cruz where a car, though nice, isn't necessary. It's a large and beautiful historic town in northern Tenerife, not overly commercial ie real people live and work there, although plenty of amenities for tourists, and in fact it became a resort a century ago - restaurants, museums, botanical gardens, zoo, small beaches, shopping, huge gorgeous pool complex designed by Cesar Manrique, IMO one of the world's greatest architects.
We stayed at Club Tarahal and loved it, I believe there are about 4 RCI resorts there, some closer to the main drags. There are buses, and many tours to other areas originate from there at low cost - another nice feature of the Canaries, the relative inexpensiveness. (Our car rental didn't seem expensive either.)
Tenerife has a national park which contains Spain's highest mountain peak - go from sea level to 11,000+ thousand feet in a couple of hours. In the winter it's snow-covered up there, after driving as far as possible we rode the cable car up, walked around in some deep but melting snow. We thought we might walk the final 500 ft to the very peak, but I was a bit dizzy, no doubt from such a quick ascent.
The only thing about northern Tenerife is less sunshine than the south - most mornings were sunny but clouds moved in during the afternoons, and a couple of times it rained - but still warm and lovely, with lots to do if you're looking for more than a sunbathing spot.
The landscapes in the north are lush, steep and amazing. We met several UK ex-pats there. If I were a resident of the EU I wouldn't mind retiring in Puerto de la Cruz!
