Where is Eidolon City?

The first thing to bear in mind with Eidolon City as a place is that it is not real. This is an important concept to grasp. Clearly it's not real as in you can find it on the atlas you have on your shelf at home, or look it up on googlemaps, but more than that, it's not real even in the universe in which this game is set.

This is because Eidolon City is an illusion. It is the world experienced by a group of people who are all in comas, scattered around the world. Everything else about Eidolon City and the world in which Eidolon City lives, is created by these people (though they do not know that that is the case).

Eidolon City is known by everyone as being a large port town in the USA on the edge of a large body of fresh water. It's one of those places that everyone knows where it is.