It is in the city of Dublin, the capital of Ireland and seat of its government. At the end of the story, the sniper "peers around the corner into O'Connell Street". O'Connell street is the main street of Dublin. In the first paragraph it says that "Around the beleaguered Four Courts the heavy guns roared." The Four Courts building housed the four courts of Ireland: the Chancery (Circuit Court, handling licensing,taxation, and any of the King's affairs), Exchequer (a superior court that dealt mostly with revenue), King's Bench (the Supreme Court), and Common Pleas ( subject vs. subject). The building was designed by James Gandon and at one time this building was considered one of the finest buildings in Dublin.
Then at the beginning of the second paragraph it says "On the rooftop near O'Connell Bridge, a Republican sniper was watching." The O'Connell Bridge was also designed by James Gandon. It flows over the River Liffey, which is also named in paragraph one.
Based on the buildings and streets surrounding this story, it appears to be an upper class neighborhood. The buildings have designers, government officials did business here, and it is the center of the capital. You will note that it says "Everywhere around was quiet. There was not much danger in going through the streets". This means that the sniper was not in much danger. All the important people had fled to safety, and the ones left were the soldiers or snipers.
However, the one woman that we meet in the story, the woman with the tattered shawl, who informs the soldiers of the sniper's position is quickly shot and her body is left in the street. No one comes to retrieve her.Those people who have stayed in this area of Dublin probably stayed in their houses and tried to stay out of the way. If they did take part, like the woman with the shawl, they took the chance of being shot. This was a sniper type war, not an all-out battle.