The National Gallery of Art is a free, wonderful, restful place to visit, in an impressive building with a huge rotunda. Here you can take a break on the big couches surrounded by beautiful art. It's just what you need after walking around Washington DC! The museum is not as crowded as other museums so you can come in the middle of the day and be fine. You don't need tickets- just walk in.

Highlights are the Monet and Van Gogh paintings, including Self-Portrait by Van Gogh.
To the west (a four minute walk), across 7th Street NW, is the National Gallery of Art Sculpture Garden (mostly modern art sculptures) with the Pavilion Cafe and a huge fountain where people ice skate in winter. Continue walking to the Smithsonian National Museum of Natural History (a seven minute walk)- you must go to see the gems! 
To the east (a four minute walk) is the National Gallery of Art East Building, mostly devoted to modern art. Make sure you walk the tunnel to this building, where you will find an amazing LED light installation called Multiverse by Leo Villareal. Walk further east and you come to the US Capitol (a thirteen minute walk from the original gallery).
To the south ( a four minute walk) is the National Air and Space Museum, a very crowded museum.

Directions

National Gallery of Art is located at 6th and Constitution Ave NW. 
Open Mon-Sat 10-5, and Sunday 11-6. 
Entrance is free and you don't need to get tickets.

Click on map for interactive view