In "By the Waters of Babylon," how can details from the story be used to identify both the time and place of the events of this story?

I can be quite specific with the place, but the time that this story takes place is going to be much more vague.

By the time that the story ends, readers know for sure that the story takes place in the future. A Great Burning is mentioned a few times in the story, and that likely refers to some cataclysmic nuclear event. A nuclear event would explain why people have been forbidden to touch metal or to go east. The metal would have been full of harmful radiation, and a radioactive cloud can remain over an area and make it inhospitable for many years. The story takes place many, many, many years after the nuclear event took place because John is able to safely travel east and touch metal. Unfortunately, the story doesn't tell us what kind of nuclear event happened. Was it a nuclear meltdown or a nuclear bombing? That would make a big difference in determining how far after the Great Burning the story takes place. For example, Hiroshima is habitable today, and it has been less than 100 years since the United States dropped the first atomic weapon there. On the other hand, Chernobyl isn't supposed to be safe for human life for another 20,000 years. Narrowing down the time setting to anything more specific than a lot of years after a nuclear holocaust is not possible.

I can be more specific with the setting location, though. John eventually travels to New York City. Readers are told that he crosses the Hudson on a raft because the bridges to the island are too broken. One specific location that John goes to is Grand Central Terminal.

I found it at last in the ruins of a great temple in the mid-city. A mighty temple it must have been, for the roof was painted like the sky at night with its stars—that much I could see, though the colors were faint and dim. It went down into great caves and tunnels—perhaps they kept their slaves there.

John thinks that it is a great temple that leads to slave tunnels, but those tunnels are actually train and subway tunnels. The ceiling in that building is indeed painted with stars. John takes eight days to walk from his village to Manhattan. If a person covers 20 to 30 miles per day, then John's village is 160 to 240 miles west of Manhattan.