Chicago has the name of the Windy City so I would say Chicago is right up there as being the Windiest place in the United States.
However there are some even windier places in the USA and one of those places that I know of is Mount Washington NH with a recorded wind speed of 35.1 MPH.
So in my opinion unless someone else can prove me wrong I would say that Mount Washington NH is the windiest place in the United States.