I think of Park City as more of a Winter kind of place. It's pretty in Summer, but after you've seen it, then what?
I've been to Yellowstone numerous times, and will be happy going back again. For as much as it doesn't change, it seems to be different each time. Each part of the Park has its own appeal, and no matter how much time you spend there, you can't see it all. Awesome place. Early Summer season will have the most baby animals to be seen.
Jackson is a great town, for what it is, and isn't. Yes, it's touristy. What else is in town to see or do? Not a lot right in the town. But outside the town, there is plenty to see. And of course, Grand Tetons National Park is pretty spectacular.
Ann-Marie, if you want to try something fun, get out a map, and look at this idea: Fly into Bozeman, Montana, rent a car, and drive down into Yellowstone through the North Entrance. (Yellowstone is a square shape, and there are five entrances - North, Northeast, East, South, and West.) There are timeshares in and near West Yellowstone, but there are also a lot of motels and B&B options. You can also book a hotel room inside the Park. Staying in West Yellowstone is the easiest way to see the Park during the day, and have a place to stay after dark.
Explore your way around Yellowstone, and when you've seen enough, drive out the South Entrance, to spend time in Grand Tetons National Park, and see Jackson. Maybe stay over a night or two. Then if you want to, drive down to Park City for another day or two. Turn in your rental car in Salt Lake City, and fly home from there.
A trip like this will give you options of seeing lots of things, but none of it will feel like it's too much to do all at once.
Dave