There are a very large number of things to do in DC that are free or very inexpensive.
You know about the Smithsonian, but do you know that there are museums off the mall that are very cool. My favorite is the little known Renwick Gallery, right off Pennsylvania Avenue a block west of the White House (still on the pedestrian only area) at 17th street. But the Museum of American Art/Portrait Gallery, as well as the Postal Museum, and the Anacostia Museum are really fascinating. And on the mall, the Freer/Sackler galleries of Asian Art and the Museum of African Art are less known, and great. Of the popular museums, I can't recommend the National Museum of the American Indian enough, as a reallly neat place to visit.
There are some government associated buildings that are less known, free, and interesting. The National Archives, where you can see the Declaration of Independence and the Constitution, also has some significant information on the paper train of this country. The Library of Congress has a Gutenberg Bible, as well as beautiful interior decoration and some interesting exhibits. The National Botanic Gardens are surprisingly refreshing and beautiful, and located right by the Capitol.
The Holocaust Museum, and both buildings of the National Gallery of Art are both also free, and really worth visiting.
There are also a number of lesser-known National Park Service sights - the Mary McLeod Bethune Council House is high on the list, as is the Frederick Douglass House.
And the beautiful architecture of the national houses of worship - Nataional Cathedral, National Shrine, National Islamic Center. All fantastic in its own way.
For nightlife, the Chinatown suggestion is a good one to start. There are a couple of bars and a lot of nice restaurants in the Penn Quarter/Chinatown area, and a significant number of theatres as well. Check out Ticketplace for half price tickets. It's at 7th and D, right next to Wooley Mammoth Theatre. In addition the Shaw Neighborhood and U Street Corridor, historically black neighborhood with a very rich history, is a great place to go for dinner and jazz in the evening. Adams Morgan, though, to me, is the best nightlife area in the city, especially for visitors. Go to Woodley Park Zoo metro stop, cross the Duke Ellington Bridge, and arrive at Columbia Road and 18th Street, and just walk around. A number of clubs offer live music, and many are open late, plus there are many fantastic restaurants of all kinds in the area. Try an Ethiopian Mesob!
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