It looks like you are in Orange County, NY? If you are near Monticello, NY Safety Track does Car days and isn't too expensive. It is a few hours further upstate, but closer than Watkins Glen.
http://nyst.com
Also, Lime Rock Park in Connecticut offers track days, usually as a part of a club. You should think about joining your local SCCA and signing up for one of their PDX/ HPDE days. It is probably the cheapest and safest way to approach doing a track day for someone new to the scene.
http://www.psccny.com