The story takes place in the city of Jefferson, county seat of fictional Yoknapaptawpha County, Mississippi, where so many of Faulkner's tales are set. It is believed that the area he describes mirrors the northern Mississippi location where Faulkner spent most of his life. Other works that are set in Jefferson include the reknowned "A Rose for Emily" and the full-length novel The Sound and the Fury.
The timeframe of "That Evening Sun" is as important a part of the setting as is the location. The narrative is set at the turn of the century (around 1900), with the South still struggling from the effects of the Civil War. The tumultuous relation between Negroes and whites as described in the story is an all-consuming issue of the era. The narrator, Quentin Compson, is also victimized by his environment - as a member of an old, established Southern family, he cannot adjust to the changes wrought in the South because of the War.
There is a lot of good material on the setting in which the story takes place on enotes - check the links below!