Visiting the Washington DC area?

Here are my suggestions for Metro-riding visitors:

Metro map: http://www.wmata.com/metrorail/systemmap.cfm

First suggestion: Google one of the commercial "Tour Washington DC" sites like http://www.cr.nps.gov/nr/travel/wash/sitelist.htm (no endorsement intended; it’s the only one with a conveniently short url!). Not that you’d necessarily take a tour, but you’ll see what they think are good places to see. Then you can look those up on your own.

Opinions:

The Zoo and Rock Creek Park. http://www.cr.nps.gov/nr/travel/wash/dc7.htm
If you like natural areas and walking, this is actually free except for the drinks and stuff you'll want to buy. Pretty place. (Yellowish green blob at 11 o'clock on the DC Diamond shape)
Metro: Red line, Woodley Park/Zoo stop.

Eastern Market http://www.easternmarket.net/
A huge multicultural flea market. My daughter loves this place
Blue and orange lines, Eastern Market stop.

Library of Congress http://www.loc.gov/loc/visit/center.html
You can get a tour but really don't need one as I recall, as much of the first floor is a self-guided tour area and very interesting to us geeky types. Right next door to the Supreme Court building.
Metro: Capitol South (Blue and Orange Lines) or Union Station (Red Line)

The Supreme Court http://www.supremecourtus.gov/visiting/visiting.html
Never been there (at least since I was a teenager) but it's got to be cool.
Metro: Capitol South (Blue and Orange Lines) or Union Station, Red Line

Washington Monument http://nps.gov/wamo/
Long lines but hey, it's a staple. Stairs aren't even open any more, in case you are thinking of physical fitness.
Metro: Orange and Blue lines, Smithsonian stop (and it's something of a hike from there)

Smithsonian museums http://www.si.edu/visit/tips.htm
Air and Space is the number one most visited place in Washington DC. For good reason. The more famous one (and fully equipped with snack bar, gift shops, rest rooms) is downtown, the newer and huge (dwarfs the space shuttle and the Enola Gay housed within!) but not necessarily more interesting one is out by Dulles airport (requires a car)--Called Udvar-Hazy museum. Free entry but 12 bucks to park.

Other Smithsonian museums listed here http://www.si.edu/museums/ include
several Art museums (good), Natural History (good but kind of has a 60s feel to much of it), National Postal museum (too small, not interesting for teenagers for long), Arts and Industries (Cool, kind of 60s feel to it), American Indian (I’ve heard mixed things, never been there) and of course, Museum of American History (a big winner!)

Metro: Smithsonian Stop (duh) on the Blue or Orange lines for most, but actually for Air and Space, which is on the east end, go to L'Enfant Plaza (Blue, Orange, Yellow, or Green) and go to the 7th & Maryland exit door, which is just a half a block south.

Bureau of Engraving and Printing http://www.tourofdc.org/tours/BureauOfEngravingAndPrinting/
This is where they print paper money. The tour is fun but kind of long, and that is even if you don't have a line to start it. Near the Holocaust museum, if you can take that.
Metro: Blue or Orange Lines, Smithsonian stop. Independence Avenue exit.

Holocaust Memorial Museum http://www.ushmm.org/
I haven't been here. My kids both went on school trips.
Metro: Blue or Orange Lines, Smithsonian stop. Independence Avenue exit.

International Spy Museum http://www.spymuseum.org/plan/
Very interesting, not cheap though.
Metro: Gallery Place/Chinatown (Red, Yellow, and Green lines)

Great Falls Park. http://www.nps.gov/gwmp/grfa/
You need a car to get here. If you can get here though, it's a cool, fun place to hike and see the falls and boulder hop and see the canal that Geo. Washington built before that nasty little civil conflict called the Revolution. On the Virginia side you get great views of the falls; on the Maryland side you can take a ride in a canal boat on the "real" canal, the C&O canal.

Kennedy Center http://www.kennedy-center.org/
There are some national orchestra shows on, and sometimes free shows at lunch. Just click Find a Performance.

National Geographic Society headquarters, especially Explorer's Hall.
http://www.nationalgeographic.com/museum/
This is too cool for words. Being in the headquarters of the people who send folks all around the world, making those maps, taking those pictures...they have posters of all those cool pictures up and I believe always for sale in the hall. Highly recommended.
Metro: Red Line, Farragut North stop; or Blue and Orange Lines, Farragut West stop.

Some additional possibilities with concerns as follows: (you'll need to Google them)

Teddy Roosevelt Island: Peace in the Potomac...but you need a car.
Union Station...history, nice to stop on your metro travels, but in the end it's just a train station.
Textile museum...I've never been there.
Newseum...I went when it was in Arlington (it's moved to DC) and it was too small and really mostly for those interested in journalism when I was there in Arlington.
FBI tour...we went before 9/11 and had a hugely long wait. In the end we got permission to skip most of the tour and just go to the shooting gallery at the end, and wished we'd done it literally 2 hours earlier. Do that if you can. That's the best part. The guy doing that is funny.
City Museum...Brand new, I don't know what it's like.
C&O Canal (in Georgetown)...you need to take a cab there, Metro doesn't go there.
Fredrick Douglass National Historical Site...I haven't been there.