In one weekend, even a long weekend, you won't even begin to scratch the surface, but pick-up one of the trolley's that hits the highlights around the National Mall and Arlington Nat'l. Cemetary and you can hop-off, hop-on all day long.
We found that a hand-held GPS (auto or phone) was a great help in keeping us oriented, pointing us to our next site, and deciding what was in walking distance. Also: Go online to get maps of the Metro subway system and the National Mall sites.
For Dining while at the Mall...
(1) The big cafeteria in the basement of the National Gallery of Art is the best thing going.
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Fairly good food, wide selection and decent prices.
(2) Runners-Up: The cafeterias in the American History Museum and basement of the Supreme Court.
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Nice gift shop at the Supreme Court.
(3) Restaurants: Go to Georgetown or Alexandria. Fommers (
www.frommers.com) has recommendations.
(4) Fast Food: Its hard to beat the burgers at any "Five Guys."
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There's one at the McPherson Sq. Metro exit on K Street.
It took us a week to do this:
The Mall...
(1) Smithsonian Museums (Air+Space & American History are crowd-pleasers).
(2) Capitol Hill (Congress, Library of Congress & Supreme Court).
(3) National Archives.
(4) The Memorials: Lincoln, Jefferson, Vietnam, Korea & WWII.
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Tours of the Archives & Congress can be reserved in advance at websites.
Arlington...
Take the trolly to the Tomb of the Unknowns, Kennedy graves and Robert E. Lee House.
Elsewhere...
(1) Ford's Theatre where Lincoln was shot is worth the diversion.
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See a show or tour. Cross the street to the house where he died... walk into the bedroom.
(2) The Kennedy Center: See a show or do a tour.
(3) A performance of the Capitol Steps (walk-in tickets available).
(4) White House: Reservations are a hassle... you have to go thru a member of Congress or Senator.
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You cannot bring a camera or much else, but can bring a cell phone.
Further Afield...
(1) Washington's Home at Mount Vernon: The "National Treasure" tour took us into the basement.
(2) Possible Options: The Naval Observatory and the National Zoo.
Google is your friend. Google the place names where you might go for directions+hours.