He was riding inside of SpaceShipOne when it landed at Oshkosh, which is pretty cool. What was classy is what happened afterwards. He asked that the ropes be taken down so that the kids could come up and touch the vehicle. He wanted them to experience the plane, not just see it behind ropes or in a museum. From Aviation Now:

Rutan, seeing a few generations past everyone else, said one reason he brought SpaceShipOne to the show was to give children the opportunity to touch the SS1--so they could tell their children they saw the first commercial spaceship. He asked that the ropes around the aircraft be pulled back to allow children to touch it.

BTW: SpaceShipOne will hang in a very prominent place in the Air & Space Museum, up between the Spirit of St. Louis and the Bell X-1.