Natl Portrait & American Art Museum

In a gloriously beautiful building are two free museums, the Smithsonian National Portrait Gallery and the Smithsonian American Art Museum. You don't need tickets- just walk in. These museums are a good choice in the middle of the day when other museums get crowded. The crowds here are manageable, and there are even comfy seats where you can take a rest. You can also use these museums as a place to visit at night when the other museums are closed, since they are open until 7pm.

The most interesting part of this museum is the Presidential Portraits section where you can see portraits of all fifty presidents and read information about each president. Some are done in unusual styles, such as Obama's portrait backed by bright flowers, and Clinton's portrait with giant pixels. Downstairs, follow the signs to see Michelle Obama's portrait- although her face doesn't look quite like her, the portrait is staged very nicely.
There are three other great sections to check out: folk art, which is always so cute with little landscapes and people walking around; contemporary art, which is always colorful; and portraits of famous contemporary Americans such as LL Cool J.
With stained glass, and incredible decorations, this building is worth checking out simply for the architecture. 
The garden court with its interesting criss-cross roof is a nice place to sit on a hot or cold day because it looks like you're outdoors but really you are inside the AC or heating. You can buy snacks from the cafe.
After, cross the street and enjoy a delicious chocolate shake at Shake Shack. Make sure to get the added malt- wow yum!
On Thursday afternoons there is a farmers market outside this museum.

Directions

The Smithsonian National Portrait Gallery and the Smithsonian American Art Museum are located at F Street NW and 8th Street NW. 
Open daily 11:30-7.
Admission is free. You don't need to get tickets.

Click on map for interactive view