We were out at Yellowstone and Grand Tetons National Parks in July. Yes, it was crowded.
We saw this campground as we went into Yellowstone through the East Entrance on HWY14/16/20. It is very convenient to Yellowstone and beautiful with the Buffalo Bill Reservoir in the background. We wished we had known about it before we had already made reservations elsewhere. It is very reasonable at $17.00 per night for the non/electric sites, and is open to September 30th. Most sites are first come first serve, but some are reservable. You have to make reservations for the reservable sites by Sept. 15th.
wyo-park.com - Buffalo Bill State Park make online reservations
We found the Hwy. 16 route over the Bighorn Mountains and into Cody,WY to be the most scenic and safest route to Yellowstone. HWY 16 merges with 14 and 20 and becomes HWY14/16/20 and takes you to the east entrance of Yellowstone.
Yellowstone’s East Entrance, the 50 most beautiful miles in America
Also if you have time go to Thermopolis, WY and visit the world's largest mineral hot spring at the state park. It would be really great to get in the 104 degree water mineral pool when the air is cool outside, and it is free.
If you do get to the Thermopolis area be sure to ride down the Wind River Valley Canyon Scenic-Byway between Shoshoni and Thermopolis. It is absolutely stunning.
Hope you trip is going well and have a great time.