I've looked at the Wikivoyage Get In section for Park City but it didn't have any helpful information. I'll be arriving in Salt Lake City airport and need to get to Park City but would rather not take a taxi, if possible. Are there any sensible public transport options?
Train 704 (green line) goes to Arena Station. From there you take the 701 (blue line) to the Central station.
However, the last 704 on a Sunday evening is at 07:58 PM.