The National Air and Space Museum has many of the airplanes and space craft.
Hanging from the ceiling is the world's first airplane built by the Wright brothers. Also there is Charles Lindbergh's "Spirit of St. Louis" which was the first airplane to fly across the Atlantic Ocean.
On the space front, there are many things from early space flights, including the Friendship 7 which was rode by John Glenn when he became the first American in space.
There are also many of the early space rockets, and other space equipment such as the sky lab.