The Spy Museum is great. Unlike Smithsonian and other attractions it’s privately owned and charges admission (about $12 when I was there), BUT it’s also open a lot later than the others so I’d make it your last stop. (Across the road from Spy Museum is a restaurant called ZAYTINYA’s, a Greco-Turkish place that is probably my favorite restaurant in D.C.- very moderately priced mezze/tapas style dining.)
By all means the Library of Congress- it’s a must. It’s possibly the most beautiful building in America and its exhibitions are on par with the Smithsonian (plus they always have on display a Gutenberg Bible, the contents of Lincoln’s pockets the night he was killed, etc.). Take the guided tour because there are hidden gems throughout the place in the artwork, sculpture, etc…
I’d least recommend the National Archives. The line is usually very long, you finally get to see the Constitution/Declaration for about a minute each and when you do they’re so faded you can’t read them (plus having seen the replicas of it so often it’s anticlimactic), so I’d spend the time elsewhere.
Ford’s Theater and the Petersen House are musts. The theater has a great museum about the assassination in the basement that includes, of course, the murder weapon and Booth’s other arsenal components, a hood that the conspirators were forced to wear at trial, the clothes Lincoln wore that night (with bloodstained collar), etc… The Petersen House isn’t that fascinating really, but it’s just across the street and takes a few minutes.
The Supreme Court if you get the chance- very close to the Library of Congress and across the street from the Capitol (which, just in case you aren’t aware, you have to go through your Congressional Rep to get tickets to, though so long as your name isn’t Saddam Killachristian bin-Laden or Fred Phelps it’s pretty pro-forma).
Next time I’m there I want to go to the Zoo. It’s the furthest out of the attractions in DC- I’ve been there once but got there about 30 minutes before closing, when they’d already put the pandas to bed.
While it’s part of the Smithsonian Complex, let me mention that a great place for lunch is the cafeteria in the Museum of the American Indian. It’s traditional native American dishes divvied up by region (salmon for the nw, bison for great plains, etc.)- a sampler is enough for 2 people and is about $20 and contains parts of every region.
I’ve never been to the Postal Museum, but people I know who have said it was far more interesting than they’d have suspected and that they recommend it highly.
The White House you can pretty much forget about. Even if you get tickets from your Rep they can be cancelled at the last minute with no notice, but you probably won’t get tickets for security reasons. OTOH, you’re free to stand outside the fences and with a moderately high power digital camera you can take pics through the windows- no idea why there haven’t been more assassination attempts.
Invest in a laminated folding walking map and you won’t regret it. ALWAYS STAND TO THE RIGHT ON THE TRAIN STATION ESCALATORS- by day two you’ll actually find yourself cursing tourists who don’t.
If you’re in a hurry to get someplace, D.C. has the most reasonably priced cabs of any big city I’ve ever been to, incidentally. You can get all the way across town for $10 or thereabouts.
Ah- keep Manhattan and Philly- I love me some D.C… Would live there in a heartbeat if I was just a little bit hellofalot richer.