There really are remote places on Tenerife. One is around the Taganana mountains in the northeast. Getting there isn’t easy – a bus from Puerto to San Cristóbal, then an hour-long taxi ride up the mountains. The taxi ride was ridiculously cheap so I had to over-tip. The forest is occasionally steep and rugged, with tree branches forming a curly roof over my head. It’s a long hike down to the coast, but very scenic. There’s a bus from there the south coast, and from there back to Puerto.
My other hike was from Los Silos at the northwest of the island, near the Montaña de Taco. Quite hilly, but very quiet and scenic with lots of sea views.
Finally, I went up El Teide, Tenerife’s volcano in the center of the island. I didn’t know that you have to reserve a ticket for the cable car well in advance, and there is no ticket counter there, but perseverence clicking Reload until a slot opened worked. I couldn’t get to the top of the caldera because of snow, but the views from up there are fantastic. I also didn’t know that there is no bus back in the afternoon, but I was hiking down anyway to see the bizarre rock needles in the valley anyway. Glad I didn’t wait for a bus that would never come.