The whole story is set inside a house. Either the narrator and the old man share a house or they have the relationship between a landlord and tenant.
The old man lives alone and keeps his windows and doors closed. Since the neighbors are the ones who report the police, he must be living in a well-inhabited area. Due to the quick police response, we can assume that it is located in an accessible area of the city.
The main action takes place inside the bedroom of the old man and there is not much description of the room apart from its dark ambiance. It is described as private and personal where the old man can feel safe enough to close his eyes and rest.
It is a safe haven where there is no fear. The fact that he gets brutally murdered in his own bed adds to the dark nature of the crime as it not only takes an innocent life but also destroys the sacredness of the bedroom or private space.
Much of the story traverses what the narrator is explaining but even he is not sure about his mental state. This creates a level of suspense and drama to the entire setting and the action that plays out in it.