Göbekli Tepe is a hard place to get to on your own; but it is worth the travel.
Upon arrival in Istanbul, the concierge at the hotel had a parcel already waiting for me from TSC Travel. This detailed my schedule and transportation -- flights and cars all sorted for me.
The local guide, Taha Ozyavuz, was a legend. He has lived in the area since birth, and has an acute sense of the archaeology of the site. He has spent time with Klaus Schmidt and the Dig Teams. He also knows the town of Urfa inside and out -- a real bonus when it is 45°C hot.
Ask for him if you can
At TSC Travel, Melek Ada consistently went above and beyond to make the experience a painless and positive one. She is great.
I strongly recommend this as a way to experience Göbekli Tepe.
Dr Andrew Cochrane.