Try: Catamount in Hillsdale NY -- http://www.catamountski.com
and Butternut, in Great Barrington MA -- http://www.skibutternut.com
I'm in lower Westchester and make Catamount in under 2 hours. Slightly longer drive to Butternut. Both have lots of easy terrain for kids. Catamount has one pretty steep run when you can ski on your own, and it's generally less crowded than Butternut. On the other hand, Butternut has better snowmaking.
Slightly longer drives -- around 2.5 hrs or more -- Belleayre -- http://www.belleayre.com/
Bigger area, still very kid friendly place. Horrendously ugly website but a beautiful place to ski up in the Catskills. Daytrips easily done from Westchester. Longer mileage than Butternut or Catamount, but the Thruway miles go way faster than back roads to Berkshires.
Finally you should check out NY fourth graders ski free program athttp://www.44free.com/
I don't think it's limited to NY residents; gets you 3 free lift tix at most NY ski areas. When my twins were in 4th grade we used it at Catamount, Belleayre, Windham, & Plattekill - amazing deal.