I think the contrasting blue and orange on the City of Chicago website provides a sense of pride, creativity and vitality but it doesn’t necessarily scream “Chicago” specifically. As you and others have mentioned, I probably would have stuck to a red, blue and white color scheme of the Chicago flag if I were the designer. If you study similar color implementations and pay attention to detail, you can work with highly stereotypical color schemes in a way a fresh way so that they don’t come off as, in this case, patriotic.
Compared to the United States government website with a white background and blue accents, the City of Chicago website gives the city more character. The USA.gov site was probably meant to be more neutral for its local and foreign users so that it doesn’t project any notions or impressions that come with color associations. Whereas the complementary color scheme of Chicago’s site is more inviting, as you’ve mentioned, and gets the user excited about programs and activities going on in the city.