Hi Jonathan. For self catering, you've got the choice of thousands of apartments on complexes all over the island. Problem is, most of these are in the major tourist areas and, as you want a quiet area of Tenerife, they're probably not an option.
In more rural areas of the island, there are fincas, or farmhouses, that offer accommodation. Search Google for "accommodation in fincas tenerife" (without quotes) or check out this site.
Another option is the luxury campsite. I feature three of these on my site's page about camping and, for the activities you would like to do, I reckon the best one would be Camping MontaƱa Roja, situated yards from the beach at El Medano. Okay, most of the people staying there have turned up in motorhomes or brought tents with them, but the site also features log cabins that you can stay in.