Get an epic "local" pass if they are still on sale (you don't actually need to be a local to anywhere to buy it). That pass is ~$600, blacked out most places over the holidays and a few other times. But you don't want to be skiing those times anyway, trust me.
That will let you live in/around PC/SLC and ski Park City, which has 400+ runs. You can easily spend a season exploring all of that. If you get bored, you have Crested Butte, Vail, A Basin, Keystone (no blackouts), Breck, etc to the east, and a bunch of decent Tahoe hills to the (decent long road trip) west.
SLC is not dirt cheap but you can find a little crappy place of your own for what you want to spend. Or you can get a room in a house in PC and be part of what passes for ski town life here (it's UT, so it's not too funky or crazy, but it's still a legit ski town). There are also tons of dead end seasonal jobs available if you want to make a few bucks in your spare time.
Get in really good shape this summer - weights, running, yoga. Best shape of your life, preferably. You do not want to get hurt on day 3 of your free year.
-W