Closest ones I know of are:
Thunder Ridge, Patterson NY (Putnam/Dutchess County border)
Mountain Creek, Vernon, NJ
Our family has snow-tubed at both. Mountain Creek will likely be very crowded with skiers.
A little farther afield, we've tubed at Mount Southington in CT (about 45 min east of Danbury on I-84). Also a little farther afield, you might want to see if Mt. Peter or Sterling Forest in southern Orange County have snow tubing.
Technically (though a toll bridge) Campgaw Mtn on the NJ/Rockland border (on the Jersey side) may be the closest, but I'm not sure if they offer snow tubing.
Similarly, Woodbury in CT might be just a little farther than Thunder Ridge, but not sure if they offer snow tubing either.
I don't know of any closer ones than what I listed, no skiing/snow tubing places in Westchester (nor I believe in Dutchess County for that matter) and the ones in Rockland up near Bear Mountain (which I think were just skiing) closed at least 2 or 3 decades ago.
Good luck and have fun!