A farm in the American Southern, sometime during or soon after World War II
Most of Flannery O'Connor's stories are set in the southern United States, and often in her home state of Georgia. In the case of "The Displaced Person," it's obvious we are in the South, though the exact location isn't given. In addition to insisting that she was a Catholic writer (as we discuss in "In a Nutshell"), O'Connor clearly considered herself a southern writer. She also believed that the issues she raises in her stories (racism, cruelty, religious difference, hope, etc.) are applicable to any place in time. In her essay "The Fiction Writer and His Country" she wrote,
[I]t is the peculiar burden of the fiction writer to make one country do for all and that he has to evoke that one country through the concrete particulars of a life that he can make believable. (source: Collected Works, 802)
I find it hard to believe that what is observable behavior in one section can be without parallel in another. (803)
These are fancy ways of saying that she believed that by truthfully (though not necessarily realistically – see "Writing Style" for more) representing the places and people she knew, she would automatically represent similar and universal issues with regard to people and places she didn't know.
Though the exact time period of "The Displaced Person" isn't given, the references to the Holocaust let us know that the story has to be either during or after World War II. The Guizac family is from Poland. During and shortly after World War II, the horrible events taking place in Poland pushed many Polish people to do whatever necessary to find a safe place to live.
Before World War II, many early immigrants to the US were from Western European countries (like the UK) that were largely Protestant in their religion. Protestants and other groups in America were afraid of Catholic immigrants, many of whom came from Eastern European countries (like Poland). Due to this, and other racial and religious conflicts, the United States passed legislation in 1921 and 1924 that limited the number of people who could immigrate to the US from Eastern Europe. This legislation was still in place during World War II, and led the United States to turn away many Eastern Europeans who were desperately seeking a safe refuge. Those Eastern Europeans who did make it in, like Mr. Guizac, were often victims of irrational prejudices like those we see played out in "The Displaced Person."
That's the broad, historical, "macro" setting of the book. The specific "micro" setting is equally important. In a letter to her friend Betty Hester, O'Connor wrote that the farm on which the book is set is "evil" (source: Collected Works, 970). We have to agree that the farm, under Mrs. McIntyre, is an awful place. It is a hotbed of exploitation justified by irrational prejudices based on differences of class, financial status, race, religion, and country of origin. All of this culminates in the horrifying final scene, when Mrs. McIntyre, Mr. Shortley, and Sulk deliberately fail to warn Mr. Guizac that the tractor is headed straight for his legs.