You may have to compromise a bit, or just spend a couple of days doing each others sports. The best surfing is on the west coast whereas most kiters go along the south coast. Although you can kite anywhere, the popular spots are Tavira, Faro or Alvor. If you were to stay somewhere around Lagos then Alvor is quite close and the west coast is only about 30 mins away, although you'd want to hire a car for that. Plus you'll have anything else you could want in Lagos (shops, restaurants, boat trips etc). To make travelling easier, I believe surf boards can be rented for not too much money.
There's a few schools/clubs around, but I've heard good things about these guys:
Alvor Kitesurf Center : School . Shop . Camp - Bem-vindo!