In the third season finale of Fringe, Peter uses the machine to create a bridge between the universes. I thought this room was located in the base of the Statue of Liberty, as that's where the machine was Over There. During the events leading up to the finale, the machine Over Here was also moved there, or that's what I thought. Due to this, I thought the bridged room was in the base of the Statue of Liberty.
Possibly related, some of the promotional images for season 4 include a mysterious shiny round object, which I'd assumed was a hint of what the bridge room looks like from the outside: