We are currently on the way home from an extended visit to Grand Teton and Yellowstone. We left home in NJ on May 25th and expect to be home again this coming Saturday. We never make advance reservations when we travel and had no problem getting campsites in the Grand Teton and Yellowstone area. We mainly use first come-first served campgrounds as we find it easier to get a site in them than in reservation campgrounds. We did get a site for one night in Grizzly RV Park in West Yellowstone and two nights in Rocky Mountain RV Park in Gardiner by calling a week ahead. We didn't even try to get sites inside Yellowstone this year as it was crazy crowded.
So where else did we stay?
Five nights - Baker's Hole Forest Service Campground 3 miles north of West Yellowstone.
Two nights - Rainbow Point Forest Service Campground about 8 miles North of West Yellowstone.
These two locations were good for touring the lower loop of Yellowstone.
Three nights - Colter Forest Service Campground (hard side RVs only due to bear activity in the area) 2 miles beyond Cooke City.
This location was ideal for visiting the Lamar Valley and Wolf watching. If you are interested, there is a Wolf den about a mile from the entrance road to the Slough Creek campground. We saw Wolf pups and adults, plus heard howling for the first time.
For Grand Teton, we always stay at the Gros Ventre campground. We spent 19 nights there in June. In many trips to the Park we have never had a problem getting a site at Gros Ventre. We also spent one night at Colter Bay campground (not the Colter Bay RV Park).
In addition to mainly using first come-first served campgrounds, we find that not needing hookups makes it easier to get campsites without advance reservations.