Where in NY are you? You could stay in your home state and hit up Iceface, haven't skied there yet, but I've been to Placid and it's a great town. Lots to do off the hill which may be important on this trip.
As far as VT is concerned, yes Jay has the best skiing, but you need to be able to ski the trees to truly enjoy it. There is very little off hill.
Sugarbush has great terrain variety and a fair amount of decent lodging and off hill options without feeling over run. Of the ones I've skied, it's my number 2 behind Jay as far as skiing is concerned. #1 of the ones I've skied as an overall "resort" if that matters to you. SB is IMHO the land of balance, it has a bit of everything.
Stowe/Smuggs might be a good option, unfortunately haven't skied either (on my must ski list), but I've heard great things about both mountains. Stowe is a cool town that has that "VT feel". You could stay in Stowe and ski either mountain.
I'm probably the only one that does/feels this way, but I judge all VT ski areas on a +/- scale with Killington. I consider this mountain to be dead in the middle. There are things I like about it (good terrain/lifts, fun nightlife, decent affordable lodging options, proximity to Long Trail's brewery, etc). Then there are the things I hate (crowds, poor layout to handle crowds, snow quality after crowds, price, long connecting trails, crowds). I truly have a love hate relationship with this mountain. Mountains that I find better than K-mart I visit again, those that score lower than K I stay away from. I visit K when I have a certain reason to, early/late season, trip deals, etc.
I would NOT recommend K for a beginner, despite the large selection of greens. These trails are over run and many are just connecting trails between expert runs.
Pico however may be a viable option, but I still think you'd be better off elsewhere.
If you want to really get away from it all, Burke Mountain is a fun little mountain in the middle of nowhere. There is some fun expert terrain, I honestly can't recall what the beginner terrain is like, but there is a lower "mountain" dedicated to it. Nightlife is limited, but there are some nice inns nearby for lodging. Some decent eats in the area if you know where to look (River Garden is amazing). Lifts are slow, but crowds are small. It can get very cold there.
I haven't been, but I've heard Bromley is about the sunniest location in the Northeast (ski area or otherwise). This may be beneficial if you are trying to get a noob to enjoy skiing. I think they have a fair ammount of beginner terrain.
Stay away from Stratton, Mt. Snow and I've heard Okemo. Not that great and overrun with NYC/NJ. Crowds are not a good way
to introduce someone to the sport.
Good luck in planning your vaca and have a fun trip!!