The winter season is the busiest - that is when the swallows (pensioners) from the UK, Germany, Netherlands, Sweden etc go to escape the cold winters. Many stay for three months or more.
Compared to the UK and mainland Europe the weather is FAB. I have witnessed an enormous downpour that lasted 24 hours followed by glorious sun; I have suffered the Calima which is no joke if you have asthma (a huge dust storm from the Sahara) but every day I have been there between November and March I have sunbathed, swam in the sea and walked around in my shorts. In the evening you may need a cardi or lightweight jacket and long trousers but it won't get dark until 8pm.
In November you do need to be south of the island for the weather, so you are looking in the right area. Adeje is considered more 'upmarket' but is still a continuation of Cristianos/Americas. Have a look an Google Street View or Google Earth and you'll see what I mean. It is a huge resort merging former villages.
Los Gigantes is good if you want a quieter holiday - that is to the south of Americas, a good few miles away. Palm Mar is a much newer (developing) resort to the north of Cristianos. Both Gigantes and Palm Mar have very good bus services to Cristianos and Americas - Palm Mar is nearer if you like evening entertainment and need a taxi back.
La Caleta is south of Adeje, in between Americas and Gigantes and is a small, quiet resort.
What is your age group and what are your interests? All night clubbing/all day sleeping on the beach; golf; nice, quiet hotel and a daily stroll along the prom/beach with the occasional trip.
If you can be more specific we can help you more