short-cut to: family skiing in New England, New York State, Colorado, Utah, Canada.
For family skiing in In Pennsylvania, the better-known slopes are in eastern PA in the Poconos Mountains (a mere 90 minutes drive from NYC), but western PA has some action too. Note that, in this state, a vertical drop of 1000 feet is good (compared to say, Vermont slopes with 2000+ drops, or dare we mention Colorado ski resorts, with, say 3500'); but what the heck, you get to slide down slopes and these are drive-to destinations for many families.
None of these resorts is laying on family fun in the line of, say, Vermont's Smugglers' Notch; but undoubtedly they're enjoyed by many families, and prices are generally reasonable.
Camelback Ski Resort is the largest ski area in the Poconos, with ski and snowboard school, and baby-sitting for ages 12 months and up. Jack Frost/Big Boulder dual mountain has terrain parks geared to beginners, and a "Terrain Garden" too, and kids programs for ages 3 to 10. Blue Mountain: has the biggest vert, at 1082 feet, and kids programs and baby-sitting; Elk Mountain has the highest peak (2600 feet), and 1000' vert, kids programs for ages 3 to 12, and babysitting services; Shawnee Mountain is a small ski resort but the closest to NYC, with vertical drop of 700 feet.
Western Pennsylvania has ski resorts too: for example, eight ski resorts within a hundred miles of Pittsburgh, ranging from small slopes such as Boyce Park (150-foot vertical, $8 lift ticket), to Blue Knot ski resort, in the Alleghany Mountains, which tots up the biggest vertical at 1072 feet, and is family-friendly and affordable.
Mystic Mountain rates a mention here, as part of the family-friendly Nemacolin Woodlands Resort and Spa. Five slopes, 8 trails, 25 acres; it's wee, but fun.