Park City has so many amazing hikes to choose from, it might be a little overwhelming for someone just visiting for a few days. Below is a great article on 6 day hikes ranging for easy to hard in Park City and surrounding Park City.
The snow is nearly gone and the mountains are abound in green, which means it is time to get hiking! Deer Valley Resort has some of the best hiking trails in Park City and with many options for novices to experts. They also have 3 lifts running in the summer (starting mid-June) so you can choose to hike up then ride the lift down or vice versa.
It is all detailed in this great article all about hiking at Deer Valley Resort: Guide to Deer Valley Resort Hiking