We are NY Chowhounders out here now too. Here is our list - experts please critique, we are open to anything. We have a family, so we might be a little off where you are going (don't worry, we will not get in the way as our reservations are all at 530pm for the kids sake (4 and6)).
Wed Blue Iguana (spectacular SLC Mexican reportedly just opened here in PC)
Fri Spruce (the new place in the canyons, supposed to be pretty good)
SatJ and G GRill in the St Regis (heard some reports about horrific amateur service so we may shift this one)
This may help
More specifically, I like
I have heard Chez Betty is good but have not been
I know you said all kinds but that really leaves it open...anything in particular?
Miraposa at Deer Valley is great, but really pricey. My favorite restaurant is Wahso, an asian grill on main street in Park City. Their menu changes frequently, and I've never been disappointed. Chimayo (southwestern cuisine) is also another favorite (also located on main street). FYI, we always pick up a local paper, and they have great coupons for alot of restaurants (like Wahso--buy one entree, get one 1/2 off, or free...). Have a great trip!