My favorite place to eat is the Art Museum--unless they put in one of those blessed fast food food courts. I don't like that they changed all of that and I've been to DC regularly (dad lives there) since I was 12 years old.
My favorites were the American History Museum and pre-9/11, visits the White House, the Pentagon (not on tour--my dad worked there, so I got to see more stuff) and not sure if I ever went into the Capital. They have a huge visitors area underneath it now that I have never been to. Not sure if a 9yo would be interested, but it might be a good tour for an older student.
Washington Monument is neat.
I took the kids to Mount Vernon a couple of years ago and we enjoyed that. They were buidling the big visitors center at the time, so lots more to do now.
Things that bored me--Natural History museum (figures that is my kids favorite

), Air and Space used to be fun, but it is soooo crowded now.
I like the space stuff at Kennedy Space Center in Florida better, so don't need to got here anymore. I've heard that the secondary museum over by Dulles airport is very worht the trip. They have space and room and they have (from what I hear) cooler stuff. If you can make it there, I've been told it is worth the trip. We will hit it on Spring Break in a couple of weeks.
I am sorry to not knowing good places to eat--I've always eaten at home or my dad and step-mom would take me to a nice restaurant b/c I'm very into that sort of thing.
I just try to ignore the fast food--and thus enjoy the art museum.
The ARchives has been under renovation for years---so if it is open--GOOOOO!!!!
There was something so cool about seeing very old documents as a kid.
I was non-plussed by the Library of Congress. Going to a library where you really can't look at a book wasn't much fun to me as a kid.
If you have a chance to visit your representative/congressperson---that would be neat. If anything to put a face to a name--or at least an office to some person.
The Native American museum might be worth a trip. It did not exist when I was young. We visited it--unfortunately, I don't remember much about it as I was in the beginnings of a miscarriage and was highly distracted.

I don't even remember if my kids liked it at all. But if your child is into Indian history, it might be worth passing through. The cafe was neat b/c it featured regional cooking from the various areas where tribes are located. And of course, it is my nature that if I'm going to remember anything--it is the food.
Be open to the festivities during the Cherry Blossom Festival if they happen to overlap your visit. Your hotel should have some access to that information and you may find some experiences of interest that are otherwise unavailable on a regular trip to DC.
Thanks for the reminder--we thought about going into the city on our next visit and some of the spots that folks have mentioned require a little pre-planning.
My 9yo is way into "spies" and "super secret" stuff--and I think she may like the spy museum.