How much does it cost to install vinyl siding per square 10ftx10ft in New York state

Hard to say. The best advice I can give you is to get a few estimates. Every area is different. There are also other considerations. Will there be exterior insulation?
Will wrap be installed/ Soffit/fascia? How high up, etc. Those are just a few.

Also the type of siding changes a lot. Different types have different trim details and specs. Just make sure of one thing. Whoever installs it, make sure they use vinyl starter strip and not the aluminum one. If they use the aluminum, it voids the warranty on the siding. Also If possible, try to go with "Brentwood" siding. It's one of the best quality sidings out there.