There are no "old school" arcades in Manhattan. As lordnacho1 said, the last was the Chinatown Fair, which re-opened as a particularly bad redemption-game place. The guy who owned the original Chinatown Fair opened a place way the hell out in Brooklyn that I've never been to, but from what I hear it's a modern fighting game haven, not exactly "old school."
Barcade is ok, I guess - I don't like it, personally. But, the L train is running to/from Manhattan (as are most of the trains, now) and that'll get you there. If you can't find a way to get to Funspot, Barcade is a poor, poor substitute... but you will get to see a couple dozen original cabinets.
If you're coming to the States, and you can make it up there, Funspot is *definitely* worth the time and effort. You can spend hours there not even playing the games. One of the last meccas of arcade games. There are a bunch of other things to do up there, you could make a couple of days out of it. My gf and I are planning a little jaunt up there for the spring.
I would suggest some of the locations in coastal New Jersey (the Silverball Museum, Flashbacks, etc.) but those places were the ones hit very, very hard by the storm - none of them are open as far as I know.