Been to tenerife a load of times, I go a couple of times of year to get away from work and sail like hell, for kiting there really is only one place on the island and thats El Medano, in MedanO there is the South Beach (where all the kite schools are and at least 2km of horseshoe bay, with side / side on winds.
The north beach (which doesn't have any launching spots and a big hole in the wind because of a hotel 'the atlantic playa',
and then theres Cabazo, which is where all the wave sailors go, mark shinn practices, and D'light his board shaper, has his shaping bay. Its a great place to launch from beause once you go out past the reef, its straight down wind to the south beach, so you can pull as many tricks as you want, loose as much ground up wind as you want and at the end of the session land in the south beach stop for a cortado (coffee)and watch the boyz rip.
The Wind in Medano is very on or off, when its on, it will be 18 to 25/ 28 knots so and 8.5 is perfect, when its off its 2knots and no more. On windy days it will usually build during the morning, kicking in proparly about 1.30 / 1.45pm so its worth having a twelve with you for those morning sessions.
If ya need nay more help, just post back
theres lots of great info on the net about tenerife so do a search,
PS. do you surf?