There's an intruder in the dish hut! Get over there and kill whoever it is, you fools!”— Tabitha
The broadcast building can be found at the top of Black Mountain.
The building is at the far side of the radio station area as you enter it from the road.
There are two doors and two floors to the building, the second door exits at the back and cannot be entered from the outside otherwise. It leads to a staircase which leads to Tabitha's room You need Tabitha's room key to enter though, which can be found either on Tabitha's body or placed under a small rock under the stairs of the building.
The broadcast building appears only in Fallout: New Vegas.