I believe the story, "I Stand Here Ironing," takes place in a large city. The clues are found in the following words/phrases:
The narrator (Emily's mother) races home from the streetcar after work; streetcars are found in big cities, not in small towns.
The woman who cares for Emily when she is little lives downstairs. High rise apartment buildings, especially during the time this was written, are found in cities, not in small towns, and it was not unusual for neighbors who lived somewhere in an apartment building to provide daycare for working mothers who lived in the same building, in the cities.
Nursery schools in small towns tend to be more intimate and nurturing. In this story, the nursery school a "parking place for kids." The reference to parking places could indicate a large number of cars (as in a city), but the sense of a daycare being a place for youngsters to be "stored" during the day indicates large numbers of kids and not enough people to care for them--they would only have the resources to house them, not to teach or nurture them. This speaks of a big city.
The mother takes her daughter to the clinic when she is sick. Generally clinics are found in big cities, especially where people do not have a lot of money for health care, as clinics provide the basic kind of health care at a lower price than a doctor's office, which charges more.
Finally, Emily is sent to a convalescent home to recuperate from her illness. It looks nice on the outside, but the space inside is at a premium and Emily cannot even keep letters from home. The food is unappetizing and cheap, and money to run the home is raised by rich people running charity events to keep the home afloat financially.
Tillie Olsen's "I Stand Here Ironing" is a story that could be set in many places; the only indication of where the mother and Emily live is toward the end of the narrative. There, the mother tells the school official about Emily's appearances as a comedienne:
She began to be asked to perform at other high schools, even in colleges, then at city and statewide affairs.
Since Tillie Olsen, whose own life paralleled the mother's lived in California, perhaps Emily and her mother live there, as well, for such a state would have many high schools, colleges, city and statewide events. Most likely the mother and Emily do not live in a large city because the mother has related that Emily had to be sent away to a convalescent home after she had become very ill. However, they must live in a city because she mentions having to run
"out to that huge school where she was one, she was lost, she was a drop...."
That their home may be in a suburb is possible because Olsen worked for the rights of single mothers and sympathized with the frustration of suburban women who felt placed in an oppressive role.