Hi,
for what you are looking for, I would recommend the north side of the island.
The south is much more touristy (even though as Sammie pointed out, Los Cristianos is nicer than Playa de las americas).
I went to Puerta de la Cruz in the north of the island, and really enjoyed it. It's a village with lots of hotels and restaurants etc, but still doesnt feel very touristy (i.e. no 'all day breakfasts' etc). It has a nice plaza in the middle, with restaurants nearby.
We hired a car and drove along the north of the island, passing through litle villages and very remote landscape. It was beautiful and changed my perception of the canary islands.
I've heard that the north is a bit more cloudy than the south (due to Mount Teide), but the weather was still fabulous.
Cheers,
Ragazza.