We just got back from DC a month ago. We spent 6 days there and could have spent several more.
Things I highly recommend:
-Get a private Capitol tour through your representative. By the time we knew that we did not get a White House tour, all the public Capitol tours were booked, so I emailed our local Rep's office and immediately heard back with an offer for a private tour, which we accepted. The intern spent about an hour showing us around and we moved a lot more quickly and saw a lot more than the public tours, which seemed very chaotic.
-When you are done at the Capitol, walk through the tunnel to the Library of Congress. It doesn't take too long to see the main exhibits but the architecture is AMAZING. Just gorgeous. Bonus: if you go through the tunnel, you don't have to go through another security screening.
-Don't waste your money on the hop-on-hop-off tours. They are pretty universally maligned on TripAdvisor as a waste of time and money. There is now a DC Circulator bus that goes around the monument area if you really don't want to walk (and it's cheap), but we walked from the Washington Monument to the WWII Memorial, to the Korean War Memorial, Lincoln Memorial and Vietnam Memorial in just a matter of an hour or so. It's not that bad a walk. We did not make it to the Jefferson or FDR Memorials because they're on the opposite side of the Tidal Basin and the day I had planned to walk over there (from the Bureau of Engraving & Printing) it was raining.
-Metro is super easy and very safe. We stayed at a family member's rental house in northern VA and drove to the Metro station near Springfield every morning. I never once felt unsafe.
-Take the bus tour at Arlington. It's a long walk between the sights there. It's very informative as well. You don't have to get off at all the stops, but if we'd had more time, I would've done more of them.
-My kids loved the Spy Museum. I thought it was a little pricey at about $20 each, but it was much better than I expected.
-The National Archives is a great place to go. It was amazing to see the original Declaration of Independence, Constitution and Bill of Rights.
-We enjoyed the Udvar-Hazy Air & Space Annex, but it was a hassle to get to, even with a car. On the mall, we went to the main Air & Space museum, Natural History Museum and American History Museum.
-We ate lunch in the city every day we spent there. My favorites were Shake Shack (next to the Spy Museum) and Potbelly's sandwich shop. They were some of the more affordable places we ate, as well. At Shake Shack, the 4 of us split 2 shakes and they had a water station to get free water. We also split a couple of orders of fries and had plenty. We ate at Good Eats near the Capitol and it was more expensive, but we could have shared fries - the orders were pretty big. Potbelly's was delicious, especially the brownie cookie! The one meal we ate at a Smithsonian museum was very pricey and I wouldn't do that again.