The Smithsonian Air and Space Museum is a wonderful place to spend a day; definitely one of the highlights of our trip. We spent six hours there on Saturday, and then went back a couple of days later for a quick peak and still found things that we hadn't noticed the first time around.
There are exhibits from every era of flight, including a great room focusing on the Wright Brothers to an equally great room focusing on the Apollo astronauts.
And like all Smithsonian Museums, it is free. A wonderful place, for kids of all ages.