It's often considered a part of the Smithsonian, although it actually isn't. The National Gallery of Art is actually two buildings, a more traditional West Building and a contemporary East Building.
West Building's main floor takes you chronologically through the history of painting from room to room. Some of the highlights for me are Salvador Dali's last supper, the impressionist collection, the collection of American Painters, and a set of paintings entitled "the journey of life". There is also a DaVinci, and a lot of beautiful works.
There are also sculpture galleries with a number of wonderful pieces, and the central fountain, with Mercury, is also impressive. There is a lot of interpretive information available, both in the bookstore and at the information desk, and in the various galleries. There is a fountain court at one end where free chamber concerts are held on Sunday evenings (the line forms early). Both main floor and lower galleries also provide space for special shows.
The east building is a big, breezy building designed by noted architect I.M. Pei, who also did the Louvre pyramid among other notable buildings. It is a soaring place with bridges that fly and allow you unusual views of the art, like looking down on a Calder mobile. There is a small permanent collection, but this musuem houses a lot of special exhibitions. The art here is not traditional.
Amenities here include two different museum shops. There is a large museum shop with prints, gifts, and jewelry in the West Building basement, along with a Garden Court restaurant, which is a lovely place to sit and eat. Between the lower floors of the two museums is a walkway with a large museum shop (actually two - there is a children's museum shop and an adult one). This one focuses more on books and other things, and has few prints. Here you will also find a sizeable cafeteria and gelato bar, and a large manmade waterfall, part of the I.M. Pei design that spreads light and delight all through the walkway.
Part of the walk can be via a moving walkway, which on the East side drops you at yet another small gift shop, usually selling items connected with special exhibits in the East Building.
And it's all free.
The closest metro is probably Judiciary square on the red line, but Archives/Navy Memorial and Smithsonian are among the other metro stops close to the National Gallery.
Their web site gives a lot of information, and pictures of some of the collection, at nga.gov.