We went when my son was 9, he loved it! We drove from CT, and stayed in National Harbor, which we loved. We did Air and Space downtown, as well as Udvar-Hazy (which I highly recommend!). Natural History. Spy Museum (son's favorite). Newseum (my favorite, son loved it as well). Capitol tour. Saw the White House, and the monuments. We got him a 'passport' (National Parks one) and he loved getting it stamped everywhere.
We skipped the Holocaust Museum. We felt ds could handle it, however, my paternal grandmother and great grandmothers were survivors, and this is a very emotionally charged topic for me. I have been before, and I was concerned he wouldn't be yet able to handle MY emotion. We decided a separate weekend trip just for this would be best.
And note that at Newseum there are some very graphic portrayals of some of the most horrific things of the past few decades. It's an AMAZING museum, but brings forth lots of discussion, so just be prepared for that.
We had a car with us. We tried the shuttle to the Metro, and taking the Metro in but my dh wasn't a fan of all the waiting. So after the first couple days we drove in, using Parking Panda to find a garage affordable for each day near what we were doing. That worked great, dh was happier. I would have been fine with the Metro, though the shuttle waiting was a bit of a PITA. If you're staying in the city this isn't an issue.