You ARE going to spend some time in Grand Teton National Park aren't you? From Jackson you'll be driving right through it. It would be worth your while to stop and explore this beautiful park. Gros Ventre campground in the park is fairly close to Jackson. It has 300 non-reservable dry camp spots which rarely fills. In June - it won't. Further along toward Yellowstone is Colter Bay campground - the same, 300 non-reservable sites. Right next door is Colter Bay RV where you might snag a spot if you want full hookups. The hiking is fantastic in the Tetons and the scenery is like a miniature Alps - quite different from Yellowstone.
Then continue north through the south entrance of Yellowstone. If you start out from the Tetons early morning you'll see many more critters and the traffic will be light. It's quite an experience.
