The civilization that has been destroyed in this story is our own civilization, that of the United States. The city that John calls the “Place of the Gods” is New York City. It is not necessarily easy to know that the city is New York, but it is quite clear that it is somewhere in the United States.
The way that we can tell this is by looking at the things that John finds in the Place of the Gods. The one that tells most clearly that he is in the United States is the statue that he finds. We are told that, at one place where John went,
There was also the shattered image of a man or a god. It had been made of white stone and he wore his hair tied back like a woman's. His name was ASHING, as I read on the cracked half of a stone.
We know that men in colonial times often wore long hair, or at least wigs, tied back in what could be interpreted to look like a woman’s hair. “ASHING” is clearly part of “Washington.” This shows us that this was a statue of George Washington. We are also told that there were gods named Lincoln and Biltmore. These make it clear that John is in the ruins of a city in the United States.