Although the exact setting is never specified, we can assume that The Outsiders takes place in Tulsa, Oklahoma--author S. E. Hinton's home town and the site of her high school years, from which many of the events in the story are based. No exact date is given for the novel, but it can be pinpointed to the mid-1960s (1964 or after), since the Ford Mustang--a new sports car much admired by the greasers and driven by the Socs--was not produced until late 1964. Tulsa is a cowboy town, and several of the characters, including Sodapop and Dally, are involved with horses. Dally's "rodeo partner," Buck Merrill, is described as a "tall lanky cowboy" who "dug Hank Williams." Many of the events of the novel take place outdoors, since most of the greasers are poor and come from dysfunctional families. The greasers and Socs both enjoy cruising the streets, and many are involved in illegal activities such as stealing hubcaps and shoplifting. Rumbling, or gang fights, is a way of life, and many of the boys carry knives and "heaters." Both the Socs and greasers love to hang out at the local drive-in theater, a popular entertainment spot for many teenagers of the 1960s. Other popular spots where both Socs and greasers congregate are the Dairy Queen and Tasty Freeze (ice cream food chains of the 1960s); and the Dingo, which is also a hangout in Hinton's followup novel, That was Then, This is Now (in which Ponyboy also appears).
I think you might want to check out the enotes link below. Hinton writes the book in 1967 and the references to the Beatles, "rumbles," and Elvis would put it at the mid 1960's time frame. The location would be the southwestern United States for there is talk of rodeos, but it could very well be in Oklahoma, where Hinton lived as a youth. Internally, in the work, the setting is poised between the greasers' East end of town and the Socs, who live on the wealthy West end of town. The indication we get that the setting for the greasers is any place that they will be able to coalesce socially. They seem to be mobile, waging rumbles in different locations and going to different parts of town. Their mobility is reflected in the fact that they cannot go to the West end area because of who they are and the affluency represented there.