I have watched numerous people vouch for the Grizzly Campground in West Yellowstone, and many others appear appalled at their rates.
There are two other campgrounds in West Yellowstone that everyone should consider. The "Wagon Wheel Campground" and the "Rustic Campground". Both are immaculately clean and well groomed, and less money than Grizzly. The Wagon Wheel is in easy walking distance to town, and the Rustic is just about 1/4 mile further away. Both have cabins you can rent that would make you proud to call your own. The campgrounds are older, narrower, don't have pools and stores, but they are wonderful places to stay and spend a few days.
We have stayed at both campgrounds for the last 37 years, and will stay there again. Tom and Dorit at Rustic, and Ken at Wagon Wheel take a huge amount of pride in providing a beautiful experience for everyone who stays with them. They are a family that owns both campgrounds and rely on return customers and word of mouth.
Please check them out. They are both great!