When heading to either Ankara, Konya or Adana, it's best to hitch to Nevşehir first. Just walk to the western bit of town, and start hitching on a free patch of road.
When heading to the east of Turkey from Cappadocia, you'll have to head for Kayseri first. Stand along the road that heads north out of town, towards Avanos. In Avanos, you can get on the D300 towards Kayseri.
Accommodation and Sleep
It's definitely possible to camp outside of Göreme. Just remember that the rock-formations and hills of Cappadocia are protected as a natural park, so avoid sleeping too close to the town. If you're lucky, you might even find an abandoned cave or rock-house. Just make sure to leave it intact and clean.
You can also actually find some good spots inside the city, in spite of the fact that is full of hotel, hostels and paying campings. E.g. outside of the main mosque, there is a very good place to wild camp of course without your tent, just your mat. There is a terrace, and just next to it public bathroom (abdestanhesi) roof, hidden by grape leaves nobody will see you, specially at night. You will have fresh water, bathroom and free grape at a glance, will be very safe and central in the city
- I camped on that roof for 2 nights leaving there also my backpack during the day. Nobody touched it, and people didn't tell me anything. Of course I didn't call the attention too much e.g jumping on the roof during praying time) but i'm sure lots of people saw me and didn't care about. Fedecicco
Other useful info
When in season, there are countless apricot, mulberry, almond, and walnut trees everywhere, both in the town and in the valleys around it, and nobody cares if you eat as much as you like.