I was there last year and am going back this year in September.
Basically you need to be in the south. In the Bonifacio area there's about 4 spots you can go to depending on the direction of the wind. With western winds you need to be on the west side of the island; La Tonarra if you're fearless or Figari of you're a bit less adventurous. At La Tonarra you're kiting on the sea, but there's a lot of big rocks just under the water line. With western winds there's waves (rollers). There's also a rock island just before the beach, which makes starting a bit more difficult. To get there you take the road out of bonifacio along the coastline, that goes to Propriano. After a few km's you'll pass a small sign on your left pointing to La Tonarra. There's a restaurant right next to the beach. You should be able to spot it from the top as the road is at that point quite high above sealevel.
At Figari, you start in a bay (no kitesurfing allowed during july/august I've been told), but if you want more regular wind you can go out of the small bay towards the open sea. Within the bay, the water is flat. To get there, you take the same road as for La Tonnara, but keep going a bit further. When you see some kind windsurfing sign on your left, you need to go left. Then at the the first intersection left again. You'll get to a small bay with some boats. Keep going straight here onto the sand road until you come to a bay with a small wood shack at the far end. There's some grassy parts here.
With winds coming from eastern directions it's better to go to the other side of the island. At Santa Manza there's a big open bay where you can start in two different places. One is all the way at the end of the bay. There's a small sandy beach, but not a lot of wind. The other is on the side of the bay. There's a couple tiny beaches where you can start from. Far from ideal to launch a kite. For windsurfing it's pretty good there. There's quite a big swell when the wind comes in from the east or north east.
Then there's Piantarella. This is one of the most beautiful places to kite/windsurf on the island. It looks almost tropical with nice clearblue water. Don't go there with west winds as it will be extremely gusty. There's a small bar and windsurf club there, though the bar is closed from lid september.
Calalonga on the west side is supposedly pretty good as well, but I didn't find the access road last year. Will look again this year.
As for sight seeing, there's a lot of truly beautiful beaches you can go to, but you need to look for them a bit. Bonifacio is a nice old town with some bars and restaurants at the marina, plus some more bars and restaurants in the old part on top of the rocks (mostly cheaper and better).
For lodging, there's a lot of campsites in the Bonifacio area. If you want to go the cheap route you can take your tent. A bit more luxury are the bungalows you can rent (eg at Pian del Fosse, Camping des Iles, Pertamina Village). The bungalows are to me the best of both worlds. You have a small house almost to keep your stuff, but they are still very affordable (300-400Ã¢â€šÂ¬/week regardless of number of occupants). You can also rent seperate houses or appartments, but these tend to be really expensive. Especially the ones at the golf course at Piantarella are great as most have their own private swimming pool...
Here's some useful links
If you want some more specific info or some pictures send me an e-mail at email@example.com