The Udvar-Hazy Center in Chantilly, Virginia, is a companion museum to the National Air & Space Museum in downtown Washington, DC. Since Udvar-Hazy is out in the suburbs, you avoid the huge crowd downtown on the Mall, just one of the reasons we enjoy it so much (or maybe that's just me). When my twins were toddlers, they loved looking UP–up at the colorful hang gliders, parachutes, and planes hanging from the ceiling. Now that they're older, they love learning how pilots control a plane and seeing all the history from hot air balloons to space travel.
Museum admission is free, but parking is $15. Parking is free if you arrive after 4:00pm (but keep in mind that the museum closes at 5:30 most days–check the website for extended hours). There is also an IMAX Theater, Planetarium and flight simulators with fees, but it's easy to have a great trip to Udvar-Hazy without spending any money besides parking.
On this last trip, we spent a lot of time seeing the Ultralight aircraft. My kids were fascinated with them. We also got to see the Space Shuttle Discovery, which we had seen flying over the DC area back in April 2012 when it came to Udvar-Hazy to stay permanently. Visiting the Human Spaceflight section is interesting with children, since they will never experience the wonder and news of space travel the way previous generations have (since NASA has retired the shuttle program).
Unique to the Udvar-Hazy Center is its Observation Tower. Take the elevator up and revel in the 360-degree views for miles around. We had a nice clear day, so we could see planes taking off and landing at Dulles International Airport close by. It was a stunning view, and it's capitvating to both kids and adults. Other favorite parts, according to my kids, were the Blackbird (my son), the Wright Brothers planes (twin A) and the Close Encounter model, where you can search for R2D2 and other items (twin B). And, not a highlight (because of its history), but they do have the actual Enola Gay on display. This is not a “lesser” museum than the downtown location. I hope you'll visit!