Salt Lake City International Airport is your only option, but it has connections to all the major US West Coast airports plus Honolulu. It’s a hub for Delta Airlines, so that’s probably where you’ll find the most convenient schedules. Southwest also flies there and is generally cheaper, but with fewer direct flights and some occasionally bizarre routing. It is exceedingly rare to see weather-induced interruptions in Salt Lake. Less than one-half of one percent of flights at Salt Lake City International experienced weather delays so you can feel pretty confident about traveling there in winter – so jet-lag and in-flight Bloody Marys permitting, you could find yourself on the slopes in the early afternoon.
The resort has multiple base areas, but what everyone calls the Park City base area is 37 mi from the Salt Lake City International Airport and 32 mi from downtown via Interstates 80 and 15; you will drive past Canyons Village which is along the way and a few miles closer.
The cheapest option to get to Park City is public transportation (there is bus service from the airport to downtown, where you transfer to a Park City-bound bus) but it takes twice as long as most other options. There are commercial services available, such as Canyon Transportation. A return trip on their shuttle bus is roughly $80 per adult and takes 45 minutes one-way, but can be a little longer as there’s a chance you’ll be sharing the ride with other customers who may need to be dropped off along the way.
Uber is available, and can be had for as low as $45 each way but the rates vary with demand. For three people, an UberX (the ‘X’ meaning a bigger car) can be around $65 but for a group, it is probably a better option than the shuttle. Uber’s only real drawback is that, depending on driver availability, you may wind up having to wait a bit longer.
Renting your own wheels is often the best way to go, particularly for families and especially if you’re planning to visit any of the other Salt Lake City-area resorts (such as Alta / Snowbird, Brighton / Solitude, or Snowbasin). Salt Lake City’s ski resorts are some of the most accessible from a major airport in North America, and Park City is no exception. There is one pass to go over but traffic generally flows and there are rarely any problems with too much snow.
Even if you only stay in Park City, you may find having your own car convenient. They can be booked online in advance and picked up at the airport where the rental car set-up is very efficient. A compact car during ski-season has been known to go for as little as $150 for a week while an all-wheel drive SUV would go for at least $350. You won’t need snow chains if you are just heading to Park City, and it’s easy to find even without Google Maps, with plenty of signs along the way, so you probably don’t need to spring for the GPS if they try to sell it to you at an extra charge.
The number of people or amount of luggage you have would really be the only reason you’d need to get an SUV. There may be snow on the highway to Park City but it is rarely significant, so any car that fits your gear and your group will be fine unless you are venturing to other resorts such as Alta / Snowbird or Brighton / Solitude. That said, if you’re not comfortable driving in any snow, then an Uber or shuttle might be the way to go.