Unlike NY and a lot of other cities, DC is "down to earth" and made for living. Besides the obvious historical and capital reasons to visit, it is a wonderful city to walk and get around giving you the ability to see a lot in a short amount of time. We have the best museums as a whole in the US and maybe world, almost all being free (including the zoo), the White House, capital, Georgetown, Mt. Vernon (George Washington's Home), monuments, etc all easily accessible by public transportation and Metro! Bethesda (right outside of DC) has something like 200+ restaurants on top of it all. Def worth a stop....
Unlike NY and a lot of other cities, DC is "down to earth" and made for living.
Except for the high rent and knowing what bad areas to avoid I used to do a lot of traveling to DC for work, and at one point considered relocating there. The insane rent prices made me rethink, as I found it cheaper just to fly up often. However, downtown DC is certainly a *must* for visiting (every American should make the pilgrimage at least once, and there's enough art and culture for foreign visitors as well).
I used to live in Alexandria,Va. and there is so much to do and see in that area that you could itterally spent weeks there and still not see it all. Mount Vernon was a very interesting tour. Also if you have a car there are battle fields like Gettysburg & Bull Run And you can like it's already been said get to almost every thing by the metro.
People watching is great in this city. You find a lot of different culture that you won't see in most places. But seriously, it's the nation's capital and has a ton to see. If you actually want to see museums and smiths, I suggest going during off peak times. EVERYONE goes to this city at some point in their lives. Even if you don't respect politics, it's still a place you should see at least once. It's dificult to get bored.
All the different Smithsonian museums including the National Zoo... Basically what everyone else here is saying.
Use Metro. Please try to plan your trip and know where you are going. I live in Northern VA and only sometimes go downtown. But for folks who commute every day dealing with tourists on Metro can be infuriating. Know where your stop is. Don't crowd the doors. Allow people to exit the trains first before you try to get on. If you are with a group (2+ persons) try to leave room for commuters to get by on escalators and sidewalks. If you need to stop (on a platform or sidewalk) please move off to the side to allow people to pass. Just be aware of your surroundings.
Enjoy your trip! And try to take in a CAPS game while your here!
One more good thing about the area is that they have pro football.basket ball and baseball teams. Probably hockey to,but I never watch that so I'm not sure.