This year it costs $110. Out of state hunters can apply for additional tags as well.
New York State Hunting License Page

As far as land access goes, there really is not much public land there. We have been on a few pieces of state land, but they get a lot of pressure. I hunt on land that we have hunted and farmed for years. It is getting more difficult every year to find places to go because our old farming friends are losing their farms. The bow season doesn't get nearly as much pressure there and you might be able to find some space on public land before the real slaughter begins.

If I was looking for an out of state hunt I don't think I'd recommend New York to someone going blindly and knows noone there. Pennsylvania would be better with more public forests and an excessive deer (and black bear) population. I'd probably be looking at Montana or Wyoming instead, although I've never done that either.

In order to return meat, I buy a cheap styrofoam cooler, fill it with backstraps and dry ice, and take it on the plane with me. The rest of it stays with dad.