I'm gonna disagree with you on Georgetown, only because
@Sabertooth said he's gonna have a 14 year old girl and an 11 year old girl with him. Georgetown is tween girl heaven. Otherwise, good advice here. Eastern Market might be good on Saturday morning just to get away from the tourist path and get a bit of local flavor, but otherwise you can skip it.
Late June is no good for one of my two standard recommendations, seeing the Supreme Court in session. But it's perfect for my other standard recommendation, hitting the monuments at night instead of during the day.
Also, the article was dead on about the waterfront/Nats Park area. It's totally transformed and worth checking out, especially in late June when it'll be all polished and ready to go for the All-Star game two weeks later. Lotta good stuff down there, and another chance to get away from the well-worn tourist path and see the rest of the city.