I stayed in Tenerife for over a month. I rented a 6th century home, owned by the sweetest old woman.
I stayed in the town of Los Silos. You can walk to several amazing beaches (15 - 30min). And you can catch a bus to bigger towns.
It is quiet. Not too many tourists. But there are so many incredible hikes that start from this town (well, more like a village.)
Here is a photo of where I stayed:
I can give you the contact info for the owner. But do understand that both him and his family do not speak English—at all.
The WiFi was good enough for me to do some dev work at the time. No recollection if it was 10mbit or not, but it was much faster than other places I’ve stayed in the area (can’t expect fast internet on islands like these.)
P.S. I negotiated the price down to somewhere between 700 - 800 euros for the month. It’s a newly remodeled studio with loft, built from volcanic rock. One of my best rental experiences ever.