The Renwick Gallery is a free Smithsonian museum. It is housed in a gorgeous 1874 building near the White House North Lawn (a two minute walk) that was called the "American Louvre." The building has a beautiful staircase leading up to a dazzling modern LED chandelier by Leo Villareal. The best thing about the gallery is its amazing temporary exhibits, which rotate about twice a year. When I was there I saw the Burning Man exhibit, which had rooms full of sculptures straight out of the desert and the Burning Man Festival. It was crowded but the crowd was hip! Check to see which special exhibits are happening and definitely make this a stop while visiting the North Lawn and Lafayette Square!
Walk twelve minutes west to the Foggy Bottom neighborhood, where you will get way better food than in the touristy areas! This is the area where international and American offices are located and where students from George Washington University hang out.

Directions

Renwick Gallery is located at 1661 Pennsylvania Ave NW, Washington, DC 20006. 
Entrance is free.
It is open daily 10-5:30. 
You don't need tickets.

Click on map for interactive view