Being one of those idiot tourists who doesn't really like Brighton, I think its hard to not go to SLC for a first trip out west.....or 3rd trip, or even your 30th trip. And if you're staying in PC, with someone who lives there, you'll have a great time for sure! Park City, as others have said is known for its Park, and The Canyons are known for a little more of a Free-Ride gig. Let it be known that both get significantly less snow than the other side of the ridge (which is only a 40-50 min drive away) at Snowbird or Brighton. I've been to snowbird when they're getting hammered with 1-2 feet of snow in a 36 hour period and PC had gotten like 5 inches.
While I've never really found too many "Shit yourself" runs at Brighton (and I've been given a few locals tours), you can find tons of GNARLY runs at Snowbird. Locals like brighton better than snowbird because the bird gets tracked out very very quickly. (I know, plus it isn't Alta, plus Brighton is more low-key.)
Plus, the SLC Airport is just way too easy to get to and from; there used to be (and may still be) a "ride when you fly" deal where you get a free lift ticket if you land that day. I always take an evening flight out of SLC and have the opportunity to ride till 1 or 2 the day I fly out.
SLC is a good call!
Traveling the States and Taking Pictures