I flew to Kapadokya in 2003 in a big Fly In organized by AOPA's of Turkey, Greece & Israel.
The presentation:
http://www.aopa.gr/en/eventsdetails.asp?NEWS_ID=4
Ankara LTAC has one or two Flying clubs.
Checkout
Menekse Aviation in the above link and give them a contact.
Mr. Erodgan Menekse should provide you the information you need.
Ankara to Kapadokya is not too far and easy to reach.
There's no AVGAS in Kapadokya Nevshehir LTAZ from what I remember.
Kapadokya greater area archaelogical sites are amazing. Do visit them.