In section one of "A Rose for Emily" by William Faulkner we get a few details, as mentioned in the fine answer from aszerdi (above), but mostly what we get is a sense that this story is set in the South based on several things.
First of all, Faulkner's description indicates the story's southern setting. The fact that Miss Emily's elaborately ornate house was built in the seventies, has a cotton gin, and was once part of a well-to-do and important neighborhood suggests the South after the Civil War. Even the word "coquettish" (though it is used to describe the decay of the house) is suggestive of a Southern belle, as is the letter Miss Emily writes in " a thin, flowing calligraphy." The portrait and the parlor are often associated with genteel southern hospitality, as well. There is also a clear reference to the Civil War when Faulkner describes Miss Emily's final resting place.
And now Miss Emily had gone to join the representatives of those august names where they lay in the cedar-bemused cemetery among the ranked and anonymous graves of Union and Confederate soldiers who fell at the battle of Jefferson.
We do know that most of the Civil War battles were fought in the South, so it is reasonable to assume Jefferson is a southern town.
The specific people mentioned in this section also indicate a setting in the South. The fact that Miss Emily has a Negro manservant also suggests the south, as does the reference to Colonel Sartoris several times in this section. The fact that the town had an edict that Negro women can only appear in public if they are wearing an apron is a rather tragic indicator of the South after the Civil War, as well.
Most importantly, the protagonist of the story is always referred to as "Miss Emily." Not Emily, not Emily Grierson, but Miss Emily. This is a clear indication that the story is set in the South.
It is true that nothing in this section of the story clearly and directly says the story takes place in the South, and none of these details would not be enough on their own to make that claim. When considered as a whole, however, it seems obvious that this story is, indeed, set in the South.