Where.

Close to the city I like mountain creek, a little bias because that is where I get my season pass. They have 40 trails and separate (the best they can) the terrain park and the all mountainers (gapers).. But the place can of course get PACKED. The gondola and high speed quads filter the traffic.They put up tons of features. If you're into park then def check out creek with it is fully open. Weekdays and mornings are your best bet, that is normal though. And night skiing of course if that is when you can shred. Creek has 1040' vertical
Then there is the catskills. Hunter mtn, belleayre, and windham are approx 2.5 hrs away from the city and those are your best bets for day trips and powder days. The Catskills are also a great close getaway for hiking and camping in the summer. Hunter is the biggest,most expensive, and gets a lot of the city and long island traffic. I cannot speak for Windham since I only skied there one night years ago. I have been choosing belleayre recently on powder days due to the college discount and overall cheaper day trip. Also, the glades are awesome after a Nor'easter.
Then, VT is 5 hrs away and def worth it for weekend trips. I have never been to Mt snow but it is the closest and I heard it gets a lot of nyc traffic. I have been to killington, never during peak times though, I heard it can get packed as well. If all the Vt resorts are fully open I would just get on google and choose which one you want to explore. Try smuggs, Stowe, Jay peak etc..

Somebody else is going to need to tackle PA which is within the 2-3 hour range from the city. I have not skied the 'dacks either.

Also late season keep an eye out for awesome deals and ski and stays at the Catskill and VT resorts.

Agree with the last response, Mountain Creek is a good choice for a day trip. Since you're only going to be here for a few days, I assume a single day trip is all you will have time for, so Vermont is probably too far away (Southern VT, aka Stratton, Snow, and Okemo are all about a 5 hour drive). Also, for day trips, check out OvRride. They do bus day trips to a few mountains. Much cheaper and easier than renting a car, and they have awesome deals on round trip bus ticket and lift ticket. http://ovrride.com/

I would say don't waste your time driving, just hop on one of the buses.

I read too fast and skipped by the part it is not a permanent move..