I think you've hit on the problem. What counts as a city? Göbekli Tepe is incredibly old, far far older than your other suggestions. But its very age makes it difficult to decipher. I believe the leading theory was that it was a religious site, attracting large groups of otherwise pastoralist/hunter gatherers at a time of ritual. Much like many interpretations of Stone Henge. Does that mean it definitely was that? The evidence is still spotty.

Çatalhöyük, on the other hand, is incredibly well preserved. It seems to have been a permanent settlement. I like it for first city, but that's just my preference.