I realize that you need to go where the jobs are in order to make it as a sound designer. I know New York and L.A. are up there, but what about Boston, Chicago, Seattle, Honolulu?
I'd argue that it seems like the best city to start your career in is the city in which you're best connected - or can become best connected - to the audio post scene. That's not to say that once you're in the door that this particular city may provide a lifetimes' worth of career opportunities, but it'd certainly be enough to get you started and get you enough of a background to make a move to a bigger, or different, geographical market.
The other factor, I'd think, is what industry you want to enter into. Games is different than film, which is different than advertising, which is different than software/rich media, and some industries are far more distributed than others.
Sorry these aren't solid answers, but all markets are different, and it depends on what you're looking for, and what stage in your life you're at. Wanting to get a killer ground-floor opp in a city that you want to settle down in and start a family in is totally different than being right out of school and wanting to relocate a few times while chasing the right upwardly-mobile opportunities.