The setting of a story is always the combination of two elements:  place and time.  "Miss Brill" is no exception; therefore, let's analyze both elements of setting in turn.

First, the place in "Miss Brill" is ironically specific and not specific at all.  It is set in France, in an unnamed town, but specifically in the "Public Gardens" of that town.  It can also be implied that it is a small French town that is coastal (in that the people can view the shore from the gardens.)  How are we sure it is in France?  Well, that is the only reason why the French term "Les Jardins Publiques" would be used.  Note the following quotation:

The blue sky [was] powdered with gold and great spots of lightlike white wine splashed over the Jardins Publiques.

This line is important to the setting because it is part of the very first line of the story and immediately establishes the specific Public Gardens as part of the not-so specific town setting in France.

What I find interesting is that no one above truly deals with the setting of TIME in "Miss Brill," which is quite important.  Probably the least important aspect of non-specific timing is that it is set in daytime at a park.  This is important because Miss Brill enjoys looking at passersby and observing them closely.  However, the most important aspect of time is that "Miss Brill" is set in the 1920s in France.  Why is this significant?  Well, Miss Brill (the character) constantly has an ominous feeling.  Why?  It is a tumultuous time in Europe! It is after World War I and before World War II.  Quite literally, it's the time "between the wars" and Miss Brill feels it.  Miss Brill is a perfect example of the "Jazz Age" of the time period. Even though it doesn't mention the year here, you can feel the tension of the time in this quotation, further you can tell it is most likely early fall:

The air was motionless, but when you opened your  mouth there was just a faint chill, like a chill from a glass of iced water before you sip, and now and again a leaf came drifting--from nowhere, from the sky.  Miss Brill put  up her hand and touched her fur.

Therefore, as you can see, "Miss Brill" is set in Europe of the 1920's.  It is set "between the wars" where we can feel the tension as readers.  It is in France, as a result of the Public Gardens being proclaimed in the French language.  All-in-all, it is a perfect short story to teach setting!

Miss Brill, the main character of the eponymous story, is an expat, or expatriate teacher. This means that she is currently living somewhere other than her country, in this case, France. We know that she is originally from England and that she teaches English in Paris. We also know that she enjoys going to the public gardens, or Les Jardins Publiques, on Sundays to watch people. The public gardens would be then the main setting of the story. 

Although it was so brilliantly fine—the blue sky powdered with gold and great spots of lightlike white wine splashed over the Jardins Publiques

You could say that the Jardins Publiques are the equivalent to parks or assembly places where people go to spend time together. In Miss Brill we learn that in this place there is music playing, and that old and young couples alike enjoy spending their Sundays there. This contrasts a lot with Ms. Brill's lonely and solitary life, as well as with the sad fact that she resorts to build imaginary situations in her mind regarding everything that she sees. This accentuates the extent to which her loneliness actually affects her. 

The primary setting for Mansfield's short story is a park.  It is in this setting where Miss Brill freely interacts with both the people around her and the conception she has created of herself in her mind.  The band playing the music and the general atmosphere helps to bring to light the conception of herself in her mind, how she sees herself, and how she sees others see herself.  The park is where most of this action happens.  It is also the location where she hears the couple deride her and mock her fur stole. This helps her to go back to her apartment, the setting where the other critical event happens.  When she puts the stole back in its box, it is in this small and rather cramped place where she hears the stole speak back to her, reflecting that her own conception of self is still distorted, even after her experiences.

The setting for Miss Brill is in France. In an unspecified town, Miss Brill goes to the Jardins Publiques. The means quite simply the Public Gardens. In the Jardins Publique, a band plays to which she goes to the gardens to hear with regularity, as they played louder on the day of the story than on the previous Sunday. In the garden, Miss Brill has a special bench from which she enjoys listening to the music and watching the other people in the park. On the day of the story, two other people are already seated on her special bench. She finds them a welcome addition and is only disappointed that they do speak.