To me, the main conflict in this story is between John and himself. It is between his desire to see what is in the Place of the Gods and his fear of what will happen to him if he goes there.
I think that the author is trying to convey to us how what we think of as progress requires us to overcome fear and superstition. John's fears are the fears of primitive people. They are the fear of things that he does not understand. But he overcomes those fears and will, therefore, be able to help his people progress.
However, this is not all to the good. I think the author is also telling us that we as people are doomed to keep making the same mistakes over and over -- John is going to start the human race back on the path that led to New York being destroyed.
There are many conflicts throughout this short story.
One of the first conflicts that readers encounter is the conflict that John has within himself. He feels a deep desire and pull to go east, but he knows that it is forbidden to go east. His father even reminds John of the rule; however, John eventually decides that he must follow his heart. His confidence in his decision is bolstered when he sees several "signs" that he interprets as evidence that he has made the right decision.
Another conflict that John has throughout the story is a simple man vs. nature survival conflict. John must protect himself against predators that attempt to kill him. For example, he shoots and kills a panther, and he is forced to avoid and run from wild dogs.
I had just found a door I could open when the dogs decided to rush.
Another conflict in the story is John's ever present fear of the "gods." John truly believes that he will die for looking at the Place of the Gods.
But, even as I thought so, I knew I could not. If I went to the Place of the Gods, I would surely die, but, if I did not go, I could never be at peace with my spirit again.
John is able to overcome that fear because his "hunger for knowledge" is greater than his fear.
A final conflict for John occurs after he learns that the "gods" were actually real humans that lived in a former great city. He wants to tell his people the truth, but his dad warns him against such actions. His father fears what the knowledge might do to his tribe and their way of life.
After that, I wished to tell all the people but he showed me otherwise. He said, "Truth is a hard deer to hunt. If you eat too much truth at once, you may die of the truth."
John agrees to keep the secret for a bit, but he does vow to go back to the city and begin gaining the lost knowledge.
The conflict of the story is that John must over come his fears and go to the city. This is needed for him to become a priest. He must go explore the city.