Playing golf in the mountains is extremely entertaining with the views and especially because the ball goes further! Park City and surrounding area are full of golf options and many are very reasonable in price.
Park City Golf Club - Public - set right in the middle of town and is really fun. It isn't the longest course but if you can stay out of the trees and figure out those greens, you can score here. Three putts or worse are very common on these undulating greens! This is the kind of course you can play every day and not get bored. If you just want to hit a bucket, they have a driving range too. Plan ahead though, it is one of the busiest courses in the state! Tee times can be made 7 days in advance at 435-615-5800 or 8 days at http://www.parkcity.org/departments/park-city-golf-club
Canyons Golf Course - They say any golf is good golf. This course would fit that description. It's a very quirky course and with limited space, they got 18 holes in there, including the 110 yard finishing hole. There's no driving range but if you're interested in just playing a new course, check it out.
The Outlaw - Located at Hideout canyon, only 9 holes, no range or practice green. I wouldn't waste your time.
Wasatch State Park - Located in Midway which is about 20 minutes or so away, Wasatch has 36 holes, driving range and food service. The lake course is great, and usually open before anything in Park City. The mountain course is really fun. You go strait up the mountain and then turn around. There's a couple really long par 5's that can be reach in two, sometimes with a shorter iron!
Soldier Hollow - A slightly longer drive from Wasatch, also has 36 holes. The Silver Course is easier and the Gold course will give the most advanced golfer all they can handle.
Crater Springs - Formerly known as Homestead, Crater Springs is a fun course with 18 holes, driving range and full and full banquet facilities.
Mountain Dell - Just down interstate 80 from Park City, Mountain Dell also has 36 holes with a lake course and Canyon Course.
These courses are great, but you will need to know someone to get on, or sometimes you can have your club pro call ahead for you if you belong to a club back home.
Park Meadows - Links style course originally designed by Jack Nicholas. Park Meadows is always in great shape and the only private course in Park City proper.
Jeremy Ranch - An Arnold Palmer design located past Kimbal Junction. Jeremy is probably the most lenient private course to get on. It is a really fun course if you can play it!
Glenwild - A Fazio designed course and always ranked #1 in the state of Utah, Glenwild is fantastic.
Promontory Ranch - Promontory's Dye course actual allows a handful of public tee times a day, but the Nicholas course is very private. Both courses are great and always in great shape.
Tuhaye - Mark O'Meara designed course with a lot of fun holes, and great views. Tuhaye is out towards Kamas.
Victory Ranch - Rees Jones designed course. Really tough course if you are spraying the ball but very fair.
Red Ledges - Another Nicholas designed course. Red Ledges also has a short course.