The Citadel is the ruins of The Pentagon which serves as the headquarters of the Capital Wasteland Brotherhood of Steel. There's also the the Combine facility.
The Pitt is what used to be the city of Pittsburgh. The Pit is a stage in Mortal Kombat in which you can knock the opponent onto a bed of spikes, the hard stone floor, or a mass of spinning blades. This Pit is a winged warrior gunning for Medusa.