For DC, the Spy Museum was better than I expected. It's not part of the Smithsonian, so there is a fee. They have a package that includes a group experience with spy-craft activities, which we enjoyed with our daughter. Based on your description of your two boys, I think this would be right up their alley. There's also a package with a walking tour of relevant sites, but it was freezing outside (literally) when we were there, so we didn't do that one. The Spy Museum is closest to the Gallery Place / Chinatown metro stop on the yellow line.
I also like to visit the National Archives occasionally. There's just something about seeing the original documents that gets to me. Archives has its own metro stop on the yellow line.
Other museums to consider on the mall are the Air & Space Museum and the Museum of American History. Maybe Natural History if you're not going to see the one in NY or if you feel a strong need to see the Hope Diamond.
You could also walk around the tidal basin and enjoy the monuments. You can see the Lincoln Memorial, Washington Monument, WWII, Jefferson, FDR, MLK, Korean War and probably a couple of others on an urban hike of about 3 miles. Or you could rent bikes from one of the Bikeshare stands and do it that way.
There's Arlington cemetery. The changing of the guard at the tomb of the unknown soldiers is very moving, and there are a lot of interesting monuments and stories behind them throughout the cemetery. Arlington is on the blue line.
The Marines do Evening Parade at 8th & I (you need tickets for this).
There's also the White House, the Capitol, Library of Congress, Supreme Court, etc -- way more than you can cover in 2.5 days, but hopefully this gives you some ideas.