I figured I'd jumpstart this forum by listing the kart tracks that I know of in NY. Please add any that I missed.
Allegany Memorial Speedway; Wellsville, NY; dirt oval;
http://www.layfieldracing.com/Black River Raceway; Wellsville, NY; dirt oval;
http://www.backriverraceway.com/Bliss International Speedway; Bliss, NY; paved oval;
http://www.blissinternationalspeedway.com/Caroga Creek Raceway; Ephratah, NY; dirt oval;
http://www.carogacreekraceway.com/Chapel Hill Raceway; Humphrey, NY; paved oval;
http://www.chapelhillraceway.com/Dodgecity Speedway; Cobleskill, NY; dirt oval;
http://www.dodgecitygokarts.com/site/dodgecity.htmFrozen Ocean; Auburn, NY; dirt oval;
http://frozen-ocean.com/kart-racing/Genesee Valley Kart Club; Avon, NY; paved oval and road course;
http://www.gvkc.org/Limerock Speedway; Caledonia, NY; dirt oval;
http://www.limerockspeedway.com/Moe's Karting World; Addison, NY; dirt oval;
http://www.moeskartingworld.com/Oakland Valley Speedway; Cuddebackville, NY; dirt oval;
http://www.oaklandvalleyspeedway.com/Oswego Kartway; Oswego, NY; dirt oval;
http://www.oswegospeedway.com/SCHEDULE/KartwaySchedule/tabid/335/Default.aspxParadise Speedway, Geneva, NY; dirt oval;
http://www.paradisespeedway.net/Poughkeepsie Raceway; Poughkeepsie, NY; paved oval;
http://poughkeepsieraceway.com/Ransomville Speedway; Ransomville, NY; dirt oval;
http://ransomvillespeedway.com/TrackInfo/karts.htmStarlight Speedway; Trumansburg, NY; dirt oval;
http://www.starlitespeedway.com/