Little is known about the history of the building. It is managed by Lavina Forbes. She did not like the Fantastic Four as tenants but kept them around. It was eventually destroyed by Doctor Doom. Afterwards, the Fantastic Four set up shop in Four Freedoms Plaza.
Lavina is an original character to the series. She is based on similar character Walter Collins.
In the Comics
It is specifically located at 42nd Street and Madison Avenue. It is located a few blocks away from the United Nations building.
The Fantastic Four own the top five floors, not rent.
The Baxter Building was destroyed by Doctor Doom's adopted son Kristoff Vernard.