Among all museums in the US, those in Washington are unique because admission is free. The National Mall is surrounded by many interesting museums you can hardly avoid. You may challenge yourself and visit them all or you can pick up depending on your interests. If museum is not your thing, there is an incredible number of memorials to see in Washington, plus the US Capitol, the Library of Congress and the National Archives for example. White House tours are also free, but subject to request through a Congress Member or your Embassy in Washington if you’re a foreigner.
Anyway, when I went to Washington two weeks ago I visited some of these places of interest. If you lack inspiration, here’s a few glimpses of things you may want to see there: