Washington D.C.~your top 2 things to do off the beaten path.
 

In the late summer/early fall.

Keep it to two, and no analyzing. Only the first 2 things that come to mind. :)

Kreeger Museum and Dumbarton Oaks

Whistler's Peacock Room in the Freer Museum

http://www.asia.si.edu/collections/americanHome.htm

and the garden next to the Hirshhorn Museum. (No, not the sculpture garden!)

Franciscan Monastery, near Catholic University.

Monticello by way of Skyline Drive.

Not really off of the beaten path but not on a lot of must see lists was the Portrait Gallery. That was my highlight of my trip. I would rank it as the best Smithsonian of the few that we saw.

The National Building Museum - worth a visit for the building itself alone, plus has interesting exhibits

http://www.nbm.org/

The Corcoran Gallery of Art - the largest non-federal museum in Washington (and it's free on Saturdays through August 29)

http://www.corcoran.org/

The old time airshow with wing walkers, antique planes, etc in Bealeton, Va (sort of a drive from DC)

http://www.flyingcircusairshow.com/

Hiking the C&O Canal Tow Path to Great Falls, especially in winter.

kmpb beat me to the Peacock Room. :-)

Hillwood (motto: Where Fabulous Lives) http://www.hillwoodmuseum.org/

Folger Shakespeare Library. With a play if possible.

National Cathedral
Museum of Crime and Punishment

Already mentioned:
Corcoran
Dumbarton Oaks

Other in DC:
Library of Congress
Renwick Gallery
Phillips Collection

Alexandria:
Woodlawn Plantation/Pope-Leighey House
River Farm (Amer Horticultural Society

Hillwood and wherever the White House dishes are displayed.

Eastern Market.

Thanks all. My friend is planning an east coast trip. I thought of Fodors right away. She appreciates all of your suggestions.

Best,

gypsy m

I third the suggestion of Whistler's Peacock Room. Truly amazing.

My other one would be the Phillips Collection at Dupont Circle.