US Capitol and Library of Congress

The best time to see the US Capitol is at sunset when the golden light enhances the wedding-cake style dome. The US Marine Band sometimes plays on the west stairs right at this time, so look up their schedule to see if you can combine your visit with one of their concerts. The reflecting pool, on the west side, looks magical at this time of day as well. A long expanse of lawn goes gradually downhill from the Capitol building to the reflecting pool, and many people sit on the wall above the lawn to watch the sunset. Walk around to the front entrance of the Capitol on the east side and you will see more gorgeous sights. The US Capitol building expands far on either side of the dome, in all its neoclassic glory. Large oblong lampposts and a pool add to the elegant effect. Cross the street and you will come to the Library of Congress. Here you can see the Neptune fountain, which is supposed to be like the Trevi fountain in Rome but is not nearly as special. The globe-style lampposts and the ornate building really make you feel like you're in Europe! Walk to the west side of the Library of Congress to enter. 

There are tunnels that connect many government buildings here so you don't have to go through security again. Also, there are cafeterias with good food in some of the buildings. 
For an amazing, free 1.5 hour tour of the US Capitol, reserve ahead on their website. You can reserve as far as three months in advance.
Near the US Capitol is: National Gallery of Art, a free museum to the west; and National Air and Space Museum, a free and very crowded museum to the west.

Directions

The US Capitol is located at on the far east end of the National Mall, at East Capitol Street NE and First Street SE. There are a few parking spaces on the west side by the reflecting pool.

Click on map for interactive view