Hi Everyone, BouncinBetty, You'll have plenty to do and see in one week.
I suggest you review the details of the public train/metro system.
www.wmata.com
One place available on a stop of the system is Arlington National Cemetery, the historic home of Robert E. Lee's wife's family. There is a great view of the city from there, massive historic sites including the Marine Corps Memorial (aka. Iwo Jima, just outside the cemetery), Kennedy sites, also the Cemetery is right beside Fort Myer, where in 1908 Orville Wright trained some of the first military pilots (and the site of the first military aviation fatality). Also on the Virginia side of the river, and not far away, but not metro accessible, is Mount Vernon the plantation dedicated to the history of George Washington.
If you are wandering outside the city, then the Smithsonian Air & Space out at Dulles is pretty impressive. Historic Leesburg VA is not far away and you can spend an easy half-day there shopping, dining, and civil war history.
The Air & Space downtown is one of the more popular ones. The Natural History is where you'll see the gemstones. American History and American Indian are both a full day too, with American History having the flag from Fort McHenry, and some significant cars.
The train stuff in Baltimore & Ellicott City are premium if you're into that stuff. It would be a full day in the car to get over and back while seeing the sites. Also the National Capitol Trolly Museum, while nice, is not really metro-accessible or near any other super-historic sites.
The Library of Congress is pretty neat. The National Arburetum. Any of the art galleries (have you ever seen a Rembrant? we have one).
If you're hoping on going up in the Washington Monument you'll have to do some research there, I haven't done it in a really long time, and I think the tickets get sold out pretty quickly each day. Incredible view from there though!
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