Surprise! While the Deputy Mayor's office was used to stand in at Mayor Lenny's office in Ghostbusters, in Ghostbusters 2 it was decided to use an interior room in the Greystone Mansion (also known as the Doheny Estate), in Beverly Hills. Some very careful exteriors were shot outside, with the intent to pass off this 1928 California home as the 1799 official home of the mayor of New York, Archibald Gracie Mansion.
Can't place it? No wonder - it's a very clever bit of Hollywood magic. Provided you've seen Ghostbusters 2, do you remember the part where the slime covered Ghostbusters are hauled before the Mayor at home, but not before being accosted by a young Bobby Brown / doorman, looking to score a proton pack for his kid brother? If you do, that's all at Greystone Mansion.
For the best deconstruction of the scene, you should read this article at Spook Central.
unFun Fact: Greystone Mansion would make a fine haunted house all on its own, as owner Ned Doheny was killed by his secretary Hugh Plunkett, in a murder-suicide. It's actually a bit of mystery, with various rumors that Ned committed suicide.
Fun Fact: The mansion features in dozens and dozens of movies and TV shows, including The Big Lebowski and Knight Rider!