That's a pretty nice list. There are so many options for NYC, but I'd probably pick Taxi Driver too. I like my New York movies to be seedy as hell...!
I like Mulholland Drive, but I'm not sure I would pick that for LA, though. I've never been to LA, but, well, I hope its not actually that bizarre. I'm not going to look behind any dumpsters!
I probably would have went with something more classic like Sunset Blvd or even later - Chinatown, or even later - Pulp Fiction.
And people can say what they will about Lost in Translation, but it was a pretty good love letter to Japan.
You're missing Blues Brothers for Chicago, though!
This was actually discussed just a little bit on a thread from almost a year ago:
http://forums.creativecow.net/readpost/267/1130