The visuals for the city, especially of the large surrounding walls, remind me of artists renderings for Roman settlements in Turkey and Syria. (Sorry can't find examples of the specific renderings I remember)

That fact that it is a port city isn't THAT significant, most cities were based on either the sea or a river for trade reasons, but the fact that it is on a strait suggests Constantinople in my mind.

This is further reinforced by the fact that Constantinople had double walls of a similar height to what GRRM mentions for Quarth, (9-15m) , and the large visible dome similar to the Hagia Sophia.

It's unlikely that he based it entirely on one city, but rather many from the region. However old Istanbul, from the Roman period or just after, would definitely be the closest in similarity that I can think of.