Last Monday we did a tour of the Capitol and also poked around the Library of Congress a bit. The LoC would have fit better a few months later because that is when the building was built and that's more about DC than US history, but it was there and the timing worked out. There's a lot to see there about the beginning of the LoC which fit the time period we're currently learning about, but again, that's US history, not DC history.
The Library of Congress is a lovely building though and we had a great time there. Except for a possible visit when I was little (I don't remember much of anything about Washington DC from that trip in 1985), I hadn't been there before and it's definitely worth a visit.
We ate lunch in the tunnels between the different LoC buildings and I recommend that too.
Capitol tours can be booked online and there are lots of different times available. You watch a movie about it and then there's about a 45-minute tour. I was quite impressed at how well they were able to get thousands of people through that building every day. There was a lot about the early history of the building but we could have visited this building at pretty much any point through the year.