Where do the scenes take place? *Spoilers*

[Masamune·1600]

Kazushige Nojima, responsible for the story behind Advent Children, wrote a breif novella called On the Way to a Smile. In addition to providing, among other things, a massive amount of background information on Denzel, On the Way to a Smile explicitly refers to the new city as Edge.

Grabbing whatever belongings they could carry, the citizens fled from the city. But they couldn't leave behind their city of steel. Maybe they thought that if they were close to it, near that monument of prosperity, they might recapture it once again. Soon after, the city of Edge was built adjacent to Midgar.

This is only one example of several official references to the city as Edge.