LA's claim to a shuttle:
The Orbiters were built in Palmdale, just northeast of LA. The primary landing site for the early missions, until KSC built the Shuttle Landing Facility, was nearby at Edwards AFB. I think it would make perfect sense for California to host Enterprise. She was never a space vehicle, but she did undertake several free flights from the back of the 747 Shuttle Carrier Aircraft. These tests were done at Edwards. California can make a decent claim for Enterprise.
Discovery was always intended for the Smithsonian. Retired NASA spacecraft are automatically transferred to their collection, and loaned out to other locations. I have no problems with that, or with Atlantis at KSC.
A shuttle in New York makes no sense to me. There's no connection to the program there. Having a shuttle in New York, Virginia, Florida, and California puts them on the coasts, with three on the east coast, and one on the west.
Houston has always been the home of the shuttle program. The program was managed at JSC, the vehicles were designed and controlled there. The astronauts lived and trained in Houston.
New York gets a shuttle, Houston gets a couple of chairs. I made the suggestion that they should be displayed on rotating bases, since we've been told to sit and spin.
Edit:
At lunch today, I was wandering around the gift shop, looking for a cheap plastic shuttle to stick out in Rocket Park, with a nice thank you note for Mr. Bolden. Sheesh, that chinese crap is overpriced. I might just do it anyway.