Sorry in advance for the long post, but wanted to help out if I can! I've lived in the DC area for over 7 years now and there are a ton of good recommendations in this chain. I will give a list of places that I always take my guests/tell them to see when here. I am a history and politics junkie, so that does impact it:
DC is very tourist friendly, so you can honestly walk or metro to pretty much any place you want to get. Most of the monuments/capitol/WH/museums are near each other and can be walked.
1) Monument walk. Absolute must. You can see pretty much all the monuments in one shot if you are willing to do some walking. Capitol building, Washington, Vietnam, Korea, Lincoln, Jefferson, FDR, MLK, World War I & II.
2) Arlington National Cemetery. Really, really puts things in perspective. See President Kennedy's grave and the Tomb of the Unknowns. Also check out the Lee mansion and Civil War Tomb at the top of the hill as well.
3) White House and Capitol. You don't have to do tours if you can't get them, but definitely walk by them and take in the history. The Supreme Court and Library of Congress are over by the Capitol too. IF you have time, the Library of Congress on the inside is gorgeous.
4) Museums - I recommend Air and Space and American History. If you do American History the top exhibits are the Star-Spangled Banner (yes, the original); and the War and Presidency exhibits. If you do Air and Space the Wright Brothers exhibit is cool as is the Apollo program exhibit. Lots of stuff used on the moon and moon rocks you can touch.
5) National Archives - GO EARLY or you will wait forever in line. But, seeing the Declaration of Independence and Constitution is awesome and well worth it.
6) Ford's Theater - where Lincoln was assassinated. Get a tour, you can see the box he was shot in, as well as the Peterson House that he died in across the street. The museum below also has the gun Booth shot Lincoln with. Pretty haunting to see.
7) Nationals Games - go check one out if they are home while you are here. Nationals Park is beautiful and it is just a fun experience. Plus, your kids will love the President's race in either the 4th or 5th inning.
As far as restaurants etc, feel free to PM me if you want some suggestions. I'm always happy to help, and there are TONS of places to eat. Literally any kind of food you want, there will be a place.
One other thing I will tell you, observe tourist protocol. When you ride the metro, if you are going to stand on the escalators - stand on the right side, and let people walk up the left side. The locals will get agitated if you block up the whole escalator. Also, I highly recommend not riding metro before 9:30 AM and not between 4:30 PM and 7:00 PM. That is rush hour and not only is it jam packed, but the locals just want to go to/home from work. Don't take up space. Most of the museums don't open until 10 AM anyways, for that very reason.