With so much to see, it's hard to know where to begin. My suggestion is to spend your first two or three days around
The National Mall, the superb boulevard stretching between
The Capitol and
The Lincoln Memorial. Along its length you will find the principal museums and public buildings in the city.
The Smithsonian Institution
This is not just one museum but several. Consider starting with The Castle for an overview of the museum system.
The Air & Space Museum
This is possibly the best aeronautical museum on the planet and forms another part of the Smithsonian. You'll find the Wright Brothers' first flyable aircraft, Lindbergh's Spirit of St. Louis, the Apollo capsule, and many, many others here.
The National Gallery
One of the best art museums you'll find anywhere, pay careful attention to the American collection.
The Museum of Natural History
There is an enormous amount here. Don't miss the Hall of Minerals where you'll find an amazing collection of gems.
The Capitol
If you can get in through security, at least see the Rotunda, which is very impressive.
The National Archives
An original copy of both the Declaration of Independence and the Constitution is on display here.
Quick Tips:
I've met many people who strongly dislike Washington, who say it feels "strange" or "oppressive"
or even "spooky", and who can't wait to get out even after admitting that they were impressed with the
place. I don't. I feel quite comfortable there. But I think I know why: it's not like other American cities.
It's not a cookie-cutter copy of the next urban monstrosity down the Interstate. Washington has a unique personality,
an identity very closely linked to its history and to its urban designer, the Frenchman, Pierre l'Enfant, for it
was he who conceived all the main thoroughfares and public spaces. This is why Pennsylvania Avenue feels a lot
more like the Champs Élysées than Fifth Avenue. This is a city built on a human scale, one that
can be appreciated at ground level; one isn't dwarfed in high-rise canyons with ne'er a glimpse of the sun or sky.
It has an intimacy about it that few other North American cities can match.
Best Way To Get Around:
I hate driving in cities I don't know, so I park and use public transport, which is a viable option here. The buses and subways (metros) will get you where you're going quickly and reasonably. Surprisingly, taxis are affordable, too.
Transport from Dulles Airport
Be careful! Remember, Dulles is some 30 miles (50 kms.) away from downtown Washington, so taxi fare is pretty high -- figure minimum. Instead, use one of the limo services that use air-conditioned vans. These transport firms have desks just outside baggage claim on the arrivals level. Some hotels lay on free airport transport, too.
There may be a city bus link, too, but I've never seen one. There is certainly no metro service out so far.