This is a tough question. The narrator, John, does not give specific names to the locations that he is travelling through. The story takes place in the future, likely after some kind of nuclear holocaust has happened. That's what the Great Burning likely is. Cities no longer exist that are full of people. The entire country is likely back to its tribal roots, and all travel is on foot.
The reader does know that John is traveling east to the Place of the Gods. He eventually gets to a river called the Ou-dis-sun.
There was the great river below, like a giant in the sun. It is very long, very wide. It could eat all the streams we know and still be thirsty. Its name is Ou-dis-sun, the Sacred, the Long.
Across the river is the giant Place of the Gods. As John explores the location, the reader is able to figure out that the river is the Hudson, and the Place of the Gods is Manhattan. He spends his time wandering around the city, and he goes into some apartments. One specific location that he visits is Grand Central Terminal. The ceiling of that building is painted with stars and constellations, and John thinks it must have been a mighty temple.
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.
As for where the story starts out, that is really tough. We know that John traveled east to get to Manhattan. We also know that it took him eight days to get there.
Toward the setting of the eighth sun, I came to the banks of the great river.
A person's average walking speed is 3 miles per hour. If John walked for 8 hours per day, that means he covered 24 miles per day. In 8 days, he would have walked 192 miles east. That puts his starting location in the middle of present day Pennsylvania.
The story opens in the forests of New York. The narrator then travels through the forest, following the old highways originally created for the residents of New York. When he gets to New York City, he crosses the Hudson River by raft and then walks into an area of which is probably Manhattan.