Hi Elf. I grew up there.

I'll think of things along the way, but if you are doing the standard Museums and Memorials, staying in town would be useful (maybe Georgetown, if you are in to the Yuppie vibe) or Alexandria for more history and boutique stores & restaurants (Ireland's Own is great fun for drinking with friends). I would stay in Alexandria or Ballston if I was going, but I have kids. There is also "National Harbor" which is in Maryland, across the river. That is a new area and I don't know if the Metro station is open there yet. Nice place for shopping, staying, eating. If I were planning such a trip, I would stay near a metro stop (
http://www.wmata.com/rail/maps/map.cfm). Near the Airport is reasonable as well (quick Metro access is a must for a DC trip). I prefer not to stay in town... but that's me. There is a hotel in Ballston that is right above a metro stop - Can't beat that for convenience (and frankly, safety).
When you tour the WhiteHouse, down the street is the Elephant & Castle. GREAT food and terrific beer selection (when I was there a few years ago). It is on PA ave right near the Old Post Office Pavilion. (Old Post is great for history & Architecture, but the stores inside weren't worth while)
Archives is awe-inspiring and nearly brought my history buff kid to tears that THIS was the ACTUAL Declaration of Independence. We love Thomas Jefferson and were in his house when it snowed - also a tear inspiring moment. There is a sculpture garden between Archives and the Mall that is a lovely spot to enjoy & people watch. I would think the Capitol is a MUST do. For the whisper walk in the dome if nothing else.

You'll see people trying it. If you stand in a spot under the dome, the acoustics are such that if someone is standing a particular distance away, they can hear you whisper to the person beside you.

Great fun. If you have the time to arrange it, find out when the Marine Corps Silent Drill Team is performing or one of the Service bands. Sometimes there are free concerts on the Capitol steps. The Drill Team would perform at the Barracks. mesmerizing.
Union Station is down near ChinaTown and you can hop a train there to NYC. Amtrak.com would show you schedules & fares. Commuter trains to NYC are common and a commuter flight wouldn't be expensive either - last I checked they were about the same price. You end up in the air for 45 min.
I'm sure I'll come up with other things. Come sit in my living room and I'll spew all sorts of information at you.

Growing up there, we ended up resenting when we had to go into town AGAIN. Now I realize how cool it was to be around all that gorgeous architecture and history.