Agree with soricobob. We are heading to Grand Teton's, Yellowstone in July 2015 as well. We booked in Oct 2014 and many sites were taken already. You need to book NOW.
As said, book the major NP's first, then plan the rest of the route. Otherwise, you will have reservations at stops along the way and no national park!
We are leaving, by the way, on July 4 from Peoria, IL. Here are our stops:
1st nite: Henderson, NE; Prairie Oasis Campgroud; 517 miles
2nd: Rawlins KOA in Rawlins, WY; 530 miles
3 nites: Coulter Bay RV park
5 nites: Fishing bridge RV park in Yellowstone
2 nites: Ponderosa campground, Cody WY
2 nites: Devils Tower KOA, Devils Tower WY
overnite on way home: Sioux Falls KOA, Sioux Falls, SD (446 miles)
Home.
Note: this is how we typically do long trips. a few longer days up front, then slowly circling the wagon back towards home.
Hope this helps.