The National Museum of American History is chock full of exhibits all pertaining to American history and culture, and it's 100% absolutely free to get in. This is one of my favorite Smithsonians, mainly because there are even exhibits in the bathrooms (on the history of plumbing in the USA, of course!) The traveling exhibits are top notch, and the recently-renovated transportation hall, now called "America on the Move" is one of the best and well-designed exhibits I've ever experienced (and I'm a curator, so I should know). Great great great museum-- don't miss this.
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