The Spitoon is the saloon that John Cassidy owns in Vault City's courtyard area.
Here one can buy his drinks at a low price. The bar was also "raided" by sergeant Stark because Joshua attacked Stark and Cassidy needed to pay for the damage.
After the Chosen One has Cassidy as a companion, the people inside will go and on the wall there will be a sign that the bar is out of business.
The Spitoon appears only in Fallout 2.