Atlanta, Georgia, 1948-1973
Atlanta, Georgia isn't a small town, but it has the hallmarks of a small Southern town, like everyone being all up in everyone else's business. Miss Daisy's concern about her privacy is a response to the fact that when anything happens, the whole town knows about it in ten minutes—and this is half a century before text messaging.
In the 1950s, Atlanta was a booming city that prided itself on being a progressive town compared to many of its neighbor in the south. It advertised itself as "The City Too Busy to Hate." People rushed to support the temple after the bombing and raised money for its repair. Dr. King was invited to speak there. Still, Jews were often denied access to the most elite social clubs, and racial segregation was alive and well. (Source)
The movie is very much old South, with its segregated neighborhoods, scenes that look hot and humid even though you can't feel them, and a grocery store called the Piggly Wiggly. For you Yankees, that's a real place. You don't get much more Southern than the Piggly Wiggly, even though there's now one in Minnesota. Shocking.
The film takes a brief detour into Alabama—Hoke's first trip out of Georgia. Hoke comments that "Alabama ain't looking like much so far." Alabama's where Hoke and Miss Daisy encounter a pair of racist cops, making them miss the relative safety of Atlanta.
In one later scene, Miss Daisy listens to Martin Luther King, Jr. speak, and the movie plays a clip of his actual speech in Atlanta, in which he says, "segregation has placed the South socially, educationally, and economically behind the rest of the nation." Miss Daisy doesn't take her place on a picket line, but the real-life struggle for civil rights plays out in the film's background.