What is the setting of Death, the High Cost of Living by Neil Gaiman?

The novel has several different settings, and begins in London, England. Mad Hettie is in London, under a bridge, waiting for the arrival of the girls that will supply her with a white dove. Once Hettie has the dove and sacrifices it, she travels to New York City in order to find Didi, the girl that is Death.

In New York, several places are visited. The first location is Sexton's apartment, followed by the city dump, where he meets Didi for the first time. Following their meeting, the two travel to Didi's apartment, above Robbins' Grocery.