You have three "regions" in Tenerife:

1. Puerto de la Cruz = many tourists, no beach, nice and scenic "suburb"
2. Santa Cruz de Tenerife = biggest town in Tenerife, nothing special, nice and scenic "suburb"
3. The South of Tenerife = many villages, many, many tourists, beaches, somewhat deserted
1. and 3. are very "touristic". The island is very nice, beautiful nature ..., but the tourist stay only in 1. and 3.!
Tourists are from Europe: Brits, Germans ...
I have spent several winter vacations on Tenerife, renting a car and driving around. In May I would rather go to France, Italy (Sardinia)...