So we trekked to the California Science Center to check it out. We got in free, but I think now the tickets are $2.
Actual tires from the shuttle.
It was fun, although I would love to see what the inside of the ship really looks like, beyond photos. I wish you could go through it.
The science center had some other exhibits, but honestly it wasn't well organized and didn't seem that impressive to us. And they relied a lot on videos to tell about exhibits, rather than letting kids experience them. Although there was a lot of hands-on stuff for the really little kids.