Hi Alhoff, don't pay any mind to the trolls, they think this place is a library, it's not, there are plenty of skiers willing to help you plan your trip.
For a two week trip you would want a good variety of ski areas available from your base.
The three spots for this would be Tahoe, Colorado or Salt Lake.
The cheapest option is SLC and it just happens to have the best snow and arguably the best terrain, with 8 resorts w/in an hour.
Check the WIki link below, go to Orbitz and stay in Sandy or Midvale, right on the border of SLC, or in SLC itself but that would probably costs a few more dollars.
The Super 8 has a bus stop across the street, but it might take almost an hour to get to the resort, it's a city bus, not a ski shuttle. And you could walk to a few restaurants at nt.
A car should cost <$30/day and is well worth it, that way you have total mobility to ski all the resorts. Otherwise you would likely have to take a cab from the airport to the hotel, 25 minutes.
For Colorado and Tahoe the resorts are >1hr away, and I'm not sure about shuttles to get to other resorts from your hotel. And if you stay slopeside anywhere, it is going to cost you.
Another Salt Lake option is to find cheap lodging in Park City itself, might be hard for 1 person, but the resorts are all closer and your transportation to the 3 resorts is no hassle.
You can fly direct from NYC to Denver and SLC, but not Tahoe. You could leave Newark at 7am on Delta and be skiing Utah by 1pm, if you rent a car, and on your last day ski until 2pm and take the 5pm home, direct.
Another way to save money is get the AmExpress credit card, it's free, and get 25K Delta miles just for signing up. Most of the tickets are more than 25K miles, but if you are flexible, you should be able to find one for 25K miles. Most of my many trips to SLC I have flown free using Delta miles. Go to Delta.com and use this link,
search for a flight and see if you can find one for 25K around when you want to go, then get the credit card, but i might take almost a month till they are in your account.
You won't find this in the "library"!