Yellow Stone is way

You can fly in SLC, and stay there for one day, then drive to Yellow Stone and Grand Teton National Park. Both of them are damn good. You can stay one or two nights in JacksonHole, where is close to Grand Teton. You can use JacksonHole as a hub to do Grand Teton.

After finish GT, drive north to YS where is 100 miles away. But the most important thing is that you'd better book a room INSIDE yellowstone right now, if you are lucky! If you end up to stay outside of the park, the daily driving will cost you tons of time because of its big size.

Minimum 7 days is required for SLC->GT->YS->SLC.