Hmm. The Museum of Flight in Seattle is getting the Shuttle Simulator. It looks a lot like a space shuttle — if you can overlook the fact that it doesn't have wings and it's made out of plywood.
However, I think the argument can be made that Houston is more entitled to it, since that's where the astronauts trained. Frankly, I'm surprised Seattle got more than a few half-used jars of Tang from NASA as we didn't have a great deal to do with the Shuttle program during it's run.