O'Henry's "The Last Leaf" is set in New York City in the year 1907. More specifically, as the narrator points out in the opening of the story, the characters live in the Greenwich Village area of New York, west of Washington Square in the lower portion of Manhattan.
The narrator describes this setting as a place of streets with sharp angles and odd curves. Because of this, the streets seem to run haphazardly and confusingly in different directions, making it easy to get lost. It is also a quaint, old-fashioned area with "eighteenth-century gables and Dutch attics." These features lend charm to the setting. The area has many dwelling places with windows that face north, and to top if off, the rents are low.
All of these features make it an ideal place for the artists who cluster in this part of Manhattan. Artists tend to make very little money, so low rents would appeal, as would chaotically arranged streets that would make it easy to elude bill collectors. Artists need northern light to paint by and are attracted by areas that are charming, features Greenwich Village has in abundance.