>>1043514OP, yellowstone is not a park for backpacking. Its flat, heavily forested, and the geysers, while cool, are packed with tourists. Traffic is ass. Not worth it, IMO
You're fine though because yellowstone is literally right next to four backpacking meccas:
the beartooths
grand teton NP
the wind river range
grand targhee (the idaho side of the tetons)
pic is wind river