As someone who lives in Utah here are some other thoughts:
The outlet mall is, well, outlets. Some people like that on vacation.
Stop at the Whole Foods in Kimball Junction (as you turn off I-80). It is screamingly expensive but is seriously the nicest WF I have ever seen.
The Natural History Museum in SLC (near the University campus just north of where I-80 comes into the SLC valley) has some great exhibits. I like the ones that focus on geology as it will give you the "lay of the land" helping you to understand the rest of what you see as you drive around. you could stop there between the airport and heading to Park City. Also, the number of prehistoric creatures they have there found right here in UT is amazing.
If you are driving south and want to spend a night in Cedar City (near Cedar Breaks National Park, about 3.5 hours south of SLC on I-15), they will have the Utah Shakespeare festival going on. There are plays by the Bard but also musicals and dramas/comedy pretty much every night. The quality of production is very, very high. If you do go there the pizza place on Center St (Centro Woodfired) is amazing and has more than just pizza.
You will be on the west side of the Wasatch range in Park City. The ski areas on the east side are also great to visit in the summer. If you go to Snowbird, you can take the tram to to top of the ski area. You will essentially be on the "other side" of the range from Park City and can look over. You will be higher than the top of the Park City ski area. If your quads are in great shape, you can walk down from the top, but if you so, stairs will remind you of this walk for several days!
I would second visiting the Olympic Ski area in Park city. If you time it right (check the website) you might see people practicing aeriels, landing in the pool.
There's things to do in Heber/Miday - you might also look at activities listed for the Homestead Resort in Heber to get some ideas of what they are suggesting.
Provo Canyon, where Bridal Veil Falls and Timpanagos Cave is also has Sundance Resort/ski area. You might see if there are any screenings or fun things going at at the Sundance Institute that is housed there (there are also some nice hikes on the Sundance ski area).
During the year there are various free screenings of Sundance films for locals in Park City and SLC. You might check the Sundance film festival website to see if there are any while you are in town.
The symphony plays at Deer Valley on and off during the summer. You might look into that.
Finally, if anyone is going to come over Labor Day weekend you MUST stop over at the sheepdog trials in Soldier Hollow. It is a TOTAL hoot. What amazing animals. It may be hot out in the sun. Next time we go I am bringing an umbrella for the sun.
Apropos of this last comment, do not come to Utah, winter, fall, summer or spring without good sunscreen.
And stay hydrated.
