Although I enjoy D.C. now as an adult I admit as a kid coming in from NoVA to go the city often felt like a chore. The key is to not emphasize how "educational" or "good for you" it is to visit the nation's capital but find things that your kids enjoy.
There are many kid-friendly attractions starting with the National Mall. If you're going there I'd personally recommend waiting until the weather gets nicer around spring unless you're going outdoor ice skating around the National Art Gallery or seeing some of the Christmas sites in town (see recent thread on Christmas in D.C.). The monuments are grand and and majestic and all but there's often a lot of walking and time outside involved if you're going around the Mall so going in nicer weather can make it more pleasant (as the hordes of your fellow tourists that time of year would agree
). A sporting event (Nats, Wizards, Mystics, Caps, or D.C. United game) or a concert is a good way to bring them into town as are events like Cirque du Soleil. There are also several museums away from the Mall that are pretty interactive and especially good for children such as the Building Museum, Spy Museum, the Newseum, Ford's Theatre, Koshland Science Museum, National Geographic Society, and Madame Tussaud's Wax Museum.
Personally I would skip Georgetown, U Street, Dupont Circle, Capitol Hill and other neighborhoods that are often better enjoyed by us grown-ups than the smaller set. Though they are great neighborhoods to see there's not as much for kids to do and they might find them a little boring until they get older.