Don’t some news types call it “Foggy Bottom”?
Foggy Bottom is a DC neighborhood on the Potomac, famous currently for being home to the United States Department of State.
The State Department is often referred to as Foggy Bottom because of its location in the Northwest DC neighborhood which bears that name. Foggy Bottom was once a swamp near the Potomac but became a fashionable residential community in the nineteenth century.
Foggy Bottom is a particular area in DC, not the entire city. It's where the State Department and other offices are located, and so Foggy Bottom is shorthand for State.