Though it seems like it should be part of the Smithsonian collection, the National Gallery of Art is a separate entity. However, it is also completely free to visit and one of the best museums in Washington DC.
The museum is split over two buildings. The main building, or West Building, houses the older art. Here you’ll find Renaissance paintings from the Old Masters like Peter Paul Rubens, Hieronymus Bosch, and even a very rare painting by Leonardo da Vinci.
The East Building seems to start with late 19th century art. Here you’ll find modern art, and famous works from artists like Pablo Picasso.
There’s also a Sculpture Garden worth wandering through. Plus, they have five cafes on site, which actually have pretty good food. It’s very easy to spend a whole day here.