Don’t go to Costa Adeje in the South, as although there are the best hotels in this area there is nowhere to go outside the hotels.
I even stayed once in the most luxurious hotel of all Canary Islands there, the Hotel Gran Bahia del Duque. (For work purposes... I didn´t pay the bill... gosh...) Outside the hotel we tried to find a place where to have dinner (as we wanted to eat outside the hotel) and it was almost impossible. There is a shopping centre with shops and everything is closed by 22.00 h... Spanish people start to have dinner by that time!
Finally we had to take the car to go to somewhere and it was also odd... 2 restaurants (very expensive & horrible!!!) and a supermarket... that’s the night life there... it´s wonderful for these people who like to stay at the hotel and relax and go to the beach and have some day excursions... but as a young person you will get bored!!
I liked the area of Puerto de la Cruz, as there you have as well as tourist stuff all these nice places local people go to have a couple of drinks or some nice food and it´s not expensive. You have bars, restaurants, discotheques and it´s great and you have a fantastic beach there as well.
There are lots of young people in this area, tourists as well as locals.
I work in tourism in Spain and know the Canary Islands very well.
If you want to party, it would be even more convenient to go to Gran Canaria instead of Tenerife, as in Gran Canaria there you have the unique and famous party area in Playa del Ingles and beaches are much better in Gran Canaria than in Tenerife (where most beaches are rocks or a mixture between sand & rocks or artificial beaches)
Have a nice trip and enjoy!!!
All Canary Islands are lovely and worth a visit.