In what two cities is the story set and do those settings have symbolic value? Could the story have been set as validly in Cleveland and Detroit? In San Francisco and Los Angeles? In New Orleans and Atlanta?
Paul's Case begins in Pittsburgh. The setting changes to New York City for the second half of the narrative.
Cather is not an author of convenience--she does not idly pick settings for simplistic reasons. The story of Paul's Case could not have been as effectively told had the two cities not been Pittsburgh and New York City.
Pittsburgh is an industrial city with a history of steel production. This sets it up as a grey, practical city--one of necessary industry, working-class families, and practicality, rather than of art and culture. Paul craves to be in the mix of things, among the rich and the glamorous, and the artistic. This is shown by the fact he ushers at Carnegie Hall, but also dawdles after his shift is over to admire the performers.
New York City is the hub of all stage-related culture (musical theatre, dramatic plays, opera, etc.) as well as known for its high-fashion, high-class people and the luxury they live in. Paul wishes to experience everything that is iconic about New York. Although there are other cities--Los Angeles or New Orleans, for example--that are known throughout the world for their lively atmosphere or luxury, the oldest and most famous continues to be New York. Also, it must be taken into account that Cather wrote this short story in the beginning of the 20th century, and while New York would still hold the grandeur it has always been known for, the same would not necessarily be true of other metropolitan areas. Similarly, while there are other cities that could fill in for the plain, practical life that Paul's family lives in Pittsburgh, there are few other cities--again, particularly in 1905, when the story was published--that would offer such a concrete example of a boring, working-class life as cold, hard, unfeeling steel.