It is an area on the western end of the deck filled with cots in which random Rivet City residents might occasionally sleep. Upon entrance you'll see a large room with desks, several cots, and tables with food. To the right there is a small room with four cots and a locker.
The common room contains two unowned beds the player can use to sleep in for free in lieu of purchasing a room at the Weatherly Hotel.
The Rivet City common room appears only in Fallout 3.