Be adventurous. If only for a minute, step out of your comfort zone and visit a "bad" area. You're not getting an accurate picture of the US if you don't go to the East part of DC or to the Bronx. Try and get away from the masses of tourists at Time Sqaure and the National Mall and see what regular people are up to. You must not limit yourself to Manhattan, especially when the subway makes getting to the other Boroughs (staten island doesn't count) so easy. Try to catch a baseball game.
Have you done it? Have you been to the grittier parts of these cities? If so, tell us about it.