wbill, are you thinking of the National Portrait Gallery and Museum of American Art? It always has interesting photo exhibits. It is a few blocks from the Leica Shop.
The National Gallery of Art on the mall has some photographic exhibits, but limited in scale.
Sadly even though the Smithsonian has perhaps the world's largest collection of photographic equipment, almost none of it is on display. A few cameras are scattered around the various museums.
The Library of Congress has a huge image collection. These are not on display to my knowledge, but the images are probably accessible with a Researchers Card which can easily be obtained. I have only accessed books, never images.