My 2 cents...
As mentioned above, if you are here to ski LCC and BCC, living in Park City is most likely not for you. In my case, I do ski Alta and the Bird often, but only when there is fresh snow, as the drive is about 40-50 minutes and can be a pain. The rest of the time I stay in PC and drive less than 5 minutes to three different resorts, and you CAN NOT beat that. Especially when PCMR has such an amazing park, DV has great tree skiing and stays relatively untouched, and the Cans has a little of everything, plus great BC access.
Basically, if you want to ski BCC/LCC, have cheaper rent, and more young people around you, Salt Lake and probably more specifically Cottonwood Heights is where you want to be. But if you want to ski as much as physically possible, with less concern for what is the "best/steepest/gnarliest/most extreme mountain in utah" you can not beat Park City as its actually feasible to go take even just one run when you live a few minutes from the resort.
Bonus... Park City kicks ass in the winter with everyone in town to party and shred and in the summer it's super quiet and relaxing. You get the best of both worlds, in my mind.