I agree with the sit-down options - if you want something directly int he museum area the Garden Cafe in the National Gallery is a delight. They have a rotating menu that corresponds with current exhibits - right now it's Italian:
Garden Café Italia
Through early spring 2012
In honor of the exhibition Antico: The Golden Age of Renaissance Bronzes as well as the Gallery's own stellar collection of Italian masterpieces, Chef Fabio Trabocchi has transformed the menu in the Garden Café. Having recently returned to DC from New York to open the highly anticipated restaurant Fiola in Penn Quarter, Chef Trabocchi has created a menu of signature Italian cuisine for the Garden Café, including a buffet as well as à la carte dishes.