When you first start reading this story, you have no idea what the setting is. All you can really tell (you think) is that it is set in the past -- in a time when people were fairly primitive. But then you start to realize that it really is not set in the past but rather in the future. By the end of the story, you will realize that it is set in and around New York City at some point in the distant future.
We know that much of the story is set in New York City itself. The rest of it is set somewhere to the west of the city. John makes his way eastward for many days toward the city, but we do not know exactly where he starts.
As for when the story is set, all we know is that it is long in the future. A terrible war has destroyed the city and has damaged the society enough that all the people in the area have regressed to a very primitive state of existence.
Upon first thought, one might think that the "Forest People" are a classic antagonist, simply because we learn that they frequently are at war with the neighboring tribes, and even hunt individuals down. As John is on his journey, he is very wary about running into the Forest People, worried that they will take him, harm him or kill him. He even refers to them as a people that is less advanced, and more unfortunate than members of his own tribe. Then there are the radiation-filled metal objects, the wild dogs, the Place of the Gods, and the Gods themselves that are painted in ominous and dangerous terms.
However, the Forest People and other items are not really a main focus of the story; rather, they are more of a side-note in the main action that occurs. Instead, focus on the ending of the story, when John realizes at last that the Gods were the ones responsible for destroying themselves, and that they were just men like he is. He realizes that "they went a dark road," turning to the vices and crimes that eventually led to their own destruction. Because of that, most of mankind was destroyed. As his father concludes at the end, they "ate knowledge too fast," and didn't temper their technology and intellegence with wisdom and compassion; this led to their destruction. If you think of the story in these terms, the main antagonist could have been men. Themselves. Embracing technology while leaving behind our humanity. Then, John's tribe had a fear of the place of the Gods and the Gods themselves; that was a factor in their lack of progression along the way, so that could be considered an antagonistic force in their lives--ignorance and fear.
I hope that those thoughts help a bit; good luck!