Lisaugene, we've just got back from 2 weeks in Las Americas, Hotel Vulcano, which would be a quick taxi ride from Adeje I guess, and there was a very big supermarket not far from us, which I walked to once. It seemed to be mainly Spanish people shopping there and it certainly wasn't aimed at tourists. I don't know the names of the roads, but the supermarket was almost opposite the El Camison hotel, any taxi driver should know that, and just a little inland from the Tenerife Princess and the Vulcano on the same road as them. It was underground, with a pharmacy on the ground floor, and the building had a big sign saying MERCADOR on it. You could hardly miss it.
The supermarket itself was one of those with huge slabs of meat hanging up, as the spanish are fond of doing. It had a big range and also if you were a customer you got some sort of parking permit or concession when you paid at the till so if you are into car hire thats a plus too. Hope this helps.