The issue of setting is an interesting one in Gordimer's work. Since the story is established as a frame story along with a fairy tale, the notion of setting is toggled a bit. The opening of the story in which the author becomes a conscious part of the story is universal, almost devoid of a specific setting. Yet, the fairy tale that constitutes the bulk of the story is heavily reminiscent of South African Apartheid setting. It is Gordimer's genius that makes the universal fairy tale bound to its setting and the authorial understanding of consciousness as one not tethered to a particular setting.
The setting of the fairy tale is ladened with details that connect it to the Apartheid condition of South Africa. One detail of this is in the exposition of the fairy tale:
There were riots, but these were outside the city, where people of another color were quartered. These people were not allowed into the suburb except as reliable housemaids and gardeners, so there was nothing to fear, the husband told the wife.
Another detail about the setting that helps to bring out the condition of Apartheid in South Africa is given later on, when the fears of "the other" become evident to the family:
Then the time came when many of the people who were not trusted housemaids and gardeners hung about the suburb because they were unemployed. Some importuned for a job: weeding or painting a roof; anything, baas, madam.
In these details, Gordimer is making direct reference to the setting of the story as something reflective of South African Apartheid and its effect on White South Africans.