For sheer accessibility, head to Mountain Creek
in NJ. It's only 50 miles from NYC, and NJ Transit has a bus that gets you from Port Authority to the mountain for $20.50 round trip. On top of that, you get a nice $10 discount on your lift ticket with a bus receipt. More info here
in Bergen County is only 20 miles north of the GWB. So if you have access to a car (as many New Yorkers like me do not), check it out.Hidden Valley
in Vernon, NJ, ought to be nice and uncrowded, as they have a membership policy (but as far as I can tell non-members can ski there as well). They're 45 miles from the GWB, only an hour out.
I learned to ski (and then taught) for 16 years at Shawnee, from when I was 3 years old, just a wee lad! Now that I've moved from Philadelphia to NYC, however, I'd say hit up the Catskills instead of the Poconos. Better mountains, same driving time, and the ski schools might
be better. I'd recommend searching for reviews of the adult beginner ski schools at Belleayre, Hunter, Windham, and Plattekill (all Catskill resorts), and comparing them to Shawnee, Elk, Camelback, Blue, and Snö (Pocono resorts). 2-turn makes a good case for Hunter with the Try-Pak. 3 non-consecutive days of lifts, lessons, and rentals for $109 just can't be beat!