I visited Park City about a year ago, and remember eating at Wasatch Brew Pub. From what I remember it was really good, and I'd go back again. I think everyone that I was with got fish and chips, so I'm afraid that's all I can recommend. They've got a nice selection of micro-brews, and the Hefe-Weizen was especially tasty. It's right on Main Street, along with several other restaurants.
http://www.wasatchbeers.com/One place I hope you don't visit is La Casita. It was without a doubt the worst service I've ever gotten at a restaurant, expensive, and the food wasn't very good either. If you see this place, run far far away.
If you're traveling to Salt Lake City from Park City, you can pass through Solitude, and go down big cottonwood canyon road. At the base of the mountain there is a great restaurant called Porcupine Grill & Pub. We stayed in Solitude, so we were about in the middle between this place and Park City. It isn't worth going out of your way to visit, but worth a stop if you can make it.
http://www.porcupinepub.com/