The City of Stone is an almost perfect copy of Kazamatsuri, only in a very simplistic manner. This causes it to not be good at replicating small details or any details at all. As explained by Suzaki, the stone city is the exact size of Kazamatsuri and expands as it expands, however, going beyond its borders could be very dangerous. The city was intended to be used as a shelter for the people of Kazamatsuri in order to save a small faction of mankind from the Key's salvation.
During the events of Rewrite, Kotarou often finds himself somehow wandering off to the city of stone. Often, when he gets there, he meets up with robed people who are part of Gaia, or else he meets up with said summoners' hounds.
Akane's Route Edit
In Akane's route, Kotarou Tennouji, Akane Senri, Shimako and Haruhiko Yoshino, along with Yoshino's entire gang, take refuge in the city of stone and start a new life there. Then, Kotarou and Akane leave the main premises of it, exiled to live somewhere away from everyone else.