An eclectic grouping can be found here at the National Gallery, including Roy Lichtenstein, Matisse, Constable and Rembrandt. Most galleries across the USA have Van Gogh, Monet and other Impressionists, and this is no exception. All of the above have outdoor sculpture gardens as well.
The Smithsonian is a real taste of American art, of course, and has presidential memorabilia and portraits. The National Air and Space Museum is in a separate building and well worth seeing.
Some may not associate Cleveland, OH with a known art gallery, but it is worth a visit. It is in most or all top 20 lists and recently had an exhibit of private collection Monets that only showed there and in London, England. This museum has an impressive collection and ever-changing exhibits like the others mentioned above. The museum sits right next to Severance Hall, home of the Cleveland Orchestra.
Not unlike the Metropolitan Museum in NYC, the Art Institute of Chicago is highly respected for its old masters, modern art, sculpture and ancient specimens, just to cover the basics. Well-known American artists exhibited here include Hopper, Casat and Grant Wood. Architecture is a large part of the Chicago museum, especially since Frank Lloyd Wright was in the city for so long. This is the second largest museum in the country after the Met in NYC.
Titian, Gainsborough, Brueghel, Hogarth, Gerard Ter Borch, Steen, van Dyck and Degas are just a few of the painters in the Getty Museum in LA. Rodin and Calder sculptures are also here among many others. There are ancient manuscripts of the gospels from the early 800s and the 12th, 13th and 14th centuries. The photography collection includes pictures from as early as 1847.
Boston, Philadelphia, Detroit and many other cities in the US have exceptional museums as well. See them whenever possible. Visits are educational, fun and enlightening.