OK...

Must see
1. Vietnam War Memorial/Constitution Gardens
2. National Art Gallery (both buildings)
3. Lincoln Memorial
4. National Air & Space Museum
5. Changing of the Guard @ Arlington Cemetery
6. National Archives
7. Federal Reserve Bank (sometimes they circulate currency by giving it away there)
8. Irish Embassy (2234 Mass. Ave. NW )
9. Library of Congress
10. Jefferson Memorial

No guilt in avoiding:
White House
Capitol Hill
Supreme Court
Smithsonian Castle
Washington Monument
DAR Museum
the rest of the Federal Triangle