Answer: Nebraska
The first allusion to this setting comes when Danny consults Ty Webb on going to college. Webb asks: "Do you want to go to college?" "In Nebraska?", Danny replies incredulously. (I will admit as a native Nebraskan that my home state does have something of a "brain drain" of students going out of state for higher education, but the honest truth is that Nebraska does have one of the highest percentages of high school graduates attending college of any state in the union, and is consistently among the top ten states in the nation for standardized test scores. Just thought I'd throw that in.) Danny is apparently bucking for a placement at the fictional "St. Copious of Northern Nebraska". Must be close to Carhenge - but that's another quiz.
The Nebraska connection comes up later when Al Czervik ends one of his exchanges with Tony: "When are you due back in Boys Town?" Boys Town is an incorporated village in suburban Omaha, Nebraska dedicated to at risk youth. Founded in 1921 by Catholic clergyman Edward J. Flanagan, the community, now known as Girls and Boys Town, was the basis of a 1938 movie starring Mickey Rooney and Spencer Tracy, with Tracy winning an Oscar for his role as Father Flanagan. Rodney Dangerfield, unfortunately, was denied this honor for "Caddyshack".