Between Los Angeles, New York and Chicago.
Full disclosure, I am a transplanted mid-westerner and I went to school in Chicago, so I am a bit partial to Chicago. Also, I was transplanted to the mid-west from northern California, and being from Norcal I despise L.A. (sort of like the Scots despise Englandshire).
I have never been to New York.
Obviously, which city is the funniest is subjective. LA has the advantage being the home of Hollywood and some of the best comedy clubs in America as well as being the destination for aspiring performers from around the world, but I will state my case for Chicago.
Chicago is not known for great stand-up, but it is known for great improv. In fact the comedy that New York is arguably best known for, Saturday Night Live, has made a living poaching talent from the Second City: http://en.wikipedia.org/wiki/List_of_alumni_of_the_Second_City . Also, Northwestern University (the place where people who couldn't get accepted into the University of Chicago end up) has a reputation for producing great comedy. David Schwimmer, Stephen Colbert, Zach Braff, Jane Curtin, Julia Louis-Dreyfus, Ana Gasteyer, Shelley Long, Gary Marshall, Tony Randall et al.
Also John Hughes set so many of his movies in the Chicago metropolitan area. Ferris Beuller's Day Off, The Breakfast Club, Sixteen Candles, National Lampoons Christmas Vacation were all set in Chicago metro and almost all the rest of his movies featured Chicago or the mid-west in some way.
Other notable 'Chicago' comedy films that I can remember liking:
The Blues Brothers
Some Like it Hot
Adventures in Babysitting
High Fidelity
Home Alone
My Big Fat Greek Wedding
Wayne's World
most Vince Vaughn films
Am I missing any good ones?
I know that I am fighting a losing battle with Los Angeles being home to Hollywood and the Laugh Factory. There are a lot of great LA comedies, The Big Lebowski and Swingers come to mind as featuring L.A. well.
I think what makes Chicago such a great place for comedy and films in general is its Midwestern setting and its very recognizable skyline. Mid-western winters instill a sharp wit in people who are strong enough to survive when Mother Nature is trying to kill you. People also seem more real in the Midwest, whereas in NY and especially in LA people seem much more shallow.
So, what say you? Which city is America's funniest?