Looking at the language and sense of longstanding tradition in Shirley Jackson's "Lottery," without foreknowledge, I would assume the story is set in the South.
First, the name of one of the boys gathering rocks at the story's beginning is Dickie Delacroix—a name of French origin; Louisiana's origins were French. The land came into the possession of America with the Louisiana Purchase (in French, Vente de la Louisiane or "Sale of Louisiana") in 1803. [Ironically, "de la croix" means "of the cross," though the behavior of the townspeople seems anything but Christian. When Dickie is mentioned, he is collecting stones for the "stoning" to take place later that day.]
We can infer that the location is rural:
Soon the men began to gather...speaking of planting and rain, tractors and taxes.
The story takes place in a village. The etymology of the word indicates that it comes from the Old French, which might again point to the South.
This is not in what might be known as "backwater" country, where civilization might not yet have progressed. The language is too sophisticated for people raised in the woods, however, there is still the use of the word "ain't." There is also the more casual use of "anybody" rather than "anyone." Mr. Summers uses these words when asking if everyone is present.
Anybody ain't here?
Lastly, there is a sense of the superstitious nature of people which might also infer that the location is somewhere outside the path of progress (where a lack of education and logic is replaced with beliefs in the supernatural). This is mentioned with the hesitancy of villagers to help with steadying "the box."
...when Mr. Summers said, "Some of you fellows want to give me a hand?" there was a hesitation before two men...came forward to hold the box steady on the stool.
Places in the South have often been associated with a slower "movement" in terms of change and modernization. Perhaps because of the industrialization of the North before the South, as well as the elevated temperatures which slowed movement down there, and the aftermath of the Civil War, change did not visit the states below the Mason-Dixon line that quickly. Though some in the story speak of the lottery being ended in other villages, this tradition shows no signs of being put aside by this village.
I would assume that the purpose of "making the setting appear familiar and ordinary" would be the author's attempt to tell the reader that this kind of "blind acceptance" can occur anywhere, even in a place that seems otherwise harmless. Except for specific instances of foreshadowing (like the boys gathering rocks and protecting their hoard from other "thieving" youngsters), the story presents a mood at the outset, of people who have known each other all their lives: who joke with each other, know who is sick, who is alone, etc. This allows the reader to be lulled into a false sense of complacency and safety, which I feel is another part of Jackson's warning to the unsuspecting reader. Where there is "evil" for everyone to see, people can unite and take a stand to stop it. When it is accepted as commonplace behavior, it is less likely that someone will speak out against it—unless it impacts that person. However, as seen with Tessie, she is a minority and no one listens to her pleas.
Jackson herself… noted: "I hoped by setting a particularly brutal ancient rite in the present and in my own village, to shock the story's readers…