Washington, DC is museum-land. Lots of museums to see, so you may want to start be researching the museums to see what exhibits interest you. You can get on a tour bus that takes you around all day for a fee, but researching what you want to see will help you maximize the time.
But some places I'd recommend:
National Art Museum. You'll get an opportunity to see some masters like Renoir in person. Outside the museum is a fantastic sculpture garden--great if it's a nice day outside.
Ripley Gallery. This is next door to the Castle (the Smithsonian Castle, which isn't a museum, so don't waste your time in it). This is very hidden, but they can have some great exhibits.
Natural History Museum. Meteors, gems, butterflies--everything of the natural world. You can see the Hope Diamond here, and there's hands on section for kids and adults who like hands on.
Spy Museum. It's a busy, frenetic museum dealing with spies, primarily of the Cold War area. If you are researching spies for any books, the bookstore is a great resource to visit.
If it's summer and crowded with kids, try these more out of the way places in VA:
George Washington Masonic Temple. Has a museum, George Washington, and a great view of the city.
Fort Ward Museum. A Civil War museum. A museum of CW artifacts and a nice park to walk around and soak up the history.
Great Falls. A state park with a spectacular waterfall.
Lurray Caverns. Out by Shenandoah National Park, so a two hour drive at least. But it's a cave, and how often do you get to see a cave?