Cascade Cafe
In the National Gallery of Art, has fast buffet style food with salads and great desserts. It's not practical to visit unless you are already in the Gallery, but that gelato really hits the spot.
The Wright Place
The food is not great fast food chains, but it is in a relaxing, plant-filled, glass atrium adjacent to the Air and Space Museum.
The larger museums have cafeterias and cafes (http://si.edu/dining/) of varying prices and quality—in general, you get what you pay for. If you're on the mall, it's either these cafeterias or the hot dog stands. Alternatively, you can march north towards the Penn Quarter and Chinatown, or better yet south to the Waterfront for some fresh-out-of-the-water crabs and other seafood.
Mitsitam Café
This is by far the new favorite on the Mall. The National Museum of the American Indian's cafe is slightly more expensive than most museum cafeterias, but with good reason. The cafeteria food thankfully does not taste like cafeteria food, and it features interesting pre-Columbian Native foods from throughout the Western Hemisphere.
Smartkart
New concept for outdoor food carts, Smartkarts have appeared recently around D.C., selling tacos, empanadas, and salads, along with organic snacks, from an eco-friendly electric vehicle.