You can thank Dinkens, Kotch, and even Guiliani for that.
I'm in a similar boat as you, since I live in New Jersey. Here carry permits are restricted to armored car security, retired police, and politically well-connected (who can prove compelling need). Of course, you could always move out of the NY area to a more gun friendly location.
Florida will issue CCW permit to non-residents (not valid in NY or NJ, though). Those are recognized by 26 other states, I believe. I applied for mine. You can send request the application to be sent by mail; you never have to go to Florida. Simply fill out the application, have it notarized, include photos and proof of firearms training, and bring the fingerprint card to any law enforcement agency (it does not have to be in your home town or state).