Katrin,
As an alum of U of Iowa (BFA, Design) who lives in DC (working in the museum
field), I am happy to let you know about special exhibits here.  Tomorrow,
the Phillips opens an exceptional show of Georgia O'Keefe.  The National
Gallery has an exhibit from the Horowitz Collectioin (American
Impressionists), and an exhibit of John Singer Sargent.  The Hirshhorn has a
good show of contemporary artists (permanent collection).  If your interest
is primarily art, don't miss the National Museum of American Art/Portrait
Gallery.  If you are interested in seeing as many museums as possible, all of
the Smithsonian museums are worth visiting.

As for the restaurant, I am not sure about the vegetarian one's in DC.
However, there are many great places to eat in DC which cater to all tastes.

Hope this helps!

John Suau