We arrived through Tenerife Sur too, but to be honest you can get pretty much anywhere within an hour anyway, it's not a huge island For me it was crazy to see how the landscape changed drastically after like 15 minutes in the car going from the south to the north; felt like ending up on a completely different continent!
We actually skipped Masca, and now I don't even know why, because we visited pretty much every other major attraction in the area between Puerto de la Cruz and Los Gigantes... I think it might have been because the Masca Gorge was closed, so we decided to go somewhere else instead? No idea But it looks extremely beautiful, and I really enjoyed the northwest part of the island in general... We main spots we went from Puerto de la Cruz were Icod de los Vinos, Garrachico, Buenavista del Norte, La Orotava, Los Realejos, Teno Rural Park, Santiago del Teide, Las Manchas, Los Gigantes, and, of course, the volcanos - Teide is a must, but my personal favourite was Chinyero volcano & Special Natural Reserve. Extremely quiet, isolated, wild, and the landscapes were absolutely breathtaking - walking through the pine forest into lava fields. I'll see if I can find a few pics on my external hard drive... As for activities other than hiking and sightseeing, we went whale and dolphin watching on a boat from Los Gigantes, quadbiking in the Teide National Park, and I also went paragliding from there.
Oh by the way - don't forget to book your permit in advance if you want to climb all the way to the peak of Teide! Only a certain number of visitors per day is allowed for conservation reasons, and the spots are filling very quickly; you need to book it online from the Reservas de Parques Nacionales at least a month or so in advance...
Food & drinks tips: my personal favourite beer there was Mahou. Try papas arrugadas with mojo rojo or almogrote. Local bananas are very sweet and tasty. Pimientos de padrón go very well with beer. Fish is amazing and you will be spoilt for choice.
You are going to have so much fun! I really loved Tenerife and would like to return some day.