We know The Outsiders is set in 1965 because S.E. Hinton says so in the FAQ page of her website (source), but not because there's any indication in the novel (though some of the slang probably seems kind of outdated). The setting is based on Hinton's hometown of Tulsa, Oklahoma, where she was living when she wrote the story as a high school student (source). Again, this is revealed in her FAQ page, not in the text.
Why is Ponyboy so vague about time and place? Maybe because he's trying to both represent and reach out to the "hundreds and hundreds of boys living on the wrong sides of cities, boys […] who jump […] at their shadows" (12.65). The vague setting helps make the book relevant for people in other places and times. It isn't just about Tulsa; it could be about your hometown too.
The bulk of the novel's action takes place over a week one fall. Since Pony is a little vague about days of the week, we'll give you a brief rundown:
Ponyboy presents his city (and other cities) as split into two zones, the East Side and the West Side. These two zones are divided by economics. In this case, East Siders don't have enough money; West Siders have plenty. Many cities are divided along economic lines, and often, broadly speaking, into an east side and a west side, like here. But, as we also know, it's never that simple. In The Outsiders, East Side and West Side function almost like symbols – symbols to represent the economic divide as Ponyboy sees it, not the complicated nature of a real city.
When Ponyboy and Johnny run off to hide in Windrixville, the story takes a turn for the pastoral. "Pastoral" basically means "of the pasture." Pastorals often feature a contrast between the country and the city. For example, in William Shakespeare's As You Like It, city characters flee to the forest, where they get new insights on life that they can take back to the city.
Sounds kind of like what happens to Pony, Johnny, and even Dallas, doesn't it? Pony and Johnny flee to the country and return to the city as changed young men. All three discover the hero inside, but even before the fire, Johnny in particular is altered. He's still desperate, but he's made the decision to face up to the killing of Bob when he returns home. He's also discovered the beauty and comfort in nature, and even in poems and books, as a result of hanging out with Ponyboy.
The "country" in The Outsiders also operates symbolically. It might represent that place in Johnny and Pony's imagination where divisions like Social and Greaser don't exist. When Pony and Johnny are talking about the country before they fall asleep in the vacant lot, Johnny says, "It seems like there's gotta be someplace without greasers or Socs, with just people. Plain, ordinary people" (3.83). And then Pony says, "Out of the big towns […]. In the country…" (3.84).
Sure enough, in the country nobody seems to know they are Greasers or think these boys are different. In the ambulance, when Ponyboy tells Jerry he's a Greaser, Jerry has no idea what he's talking about. He accepts Pony, Johnny, and Dallas at face value, based on their heroism. He doesn't think they look like hoods.
The church is smack dab in the middle of that pastoral setting, situated at the top of a hill. Pony and Johnny can feast their eyes on the countryside stretching out beneath them. Yet, they're still isolated, outside of society, just like this church. It presents a gloomy contrast to the brightness of nature around them. Pony tells us, "It was a small church, real old and spooky and spiderwebby. It gave me the creeps" (4.92). Interestingly, Pony pretty much abandoned church since his parents died, mostly because his gang won't behave there.
Like other elements in the setting, we see some symbolic action here. Pony and Johnny are, in a sense, worshipping in this church – they're worshiping nature and friendship. They're also taking refuge and engaging in meditation. The church becomes a site of redemption for them when they rescue the schoolchildren from it and discover that they're courageous and bold in a way that makes a big difference in the lives of many people.