The Smithsonian! If you're ever in Washington DC, go there.
Are you into spooky stuff? If you like ghosts, I would recommend Waverly Hills Sanitarium in Kentucky, Eastern State Penitentiary, and Penhurst Sate Hospital in Pennsylvania. There's also Alton, Illinois, which is supposed to be one of the most haunted cities in the country.
Chicago is really cool, but not a good idea if you're alone. I've always wanted to visit Hull House, but it's not in the best area and none of my friends will go with me.