Welcome to the Forum!
We stay in the Yellowstone area but outside the park every vacation (at least twice per year). Yellowstone's Edge RV park is 31 miles north of the North entrance-lots of pull-throughs and right on the river, with mountains on both sides. It's 19 miles north to Livingston, and another 23 west to Bozeman if you need a city with some size to it.
Take a look:
https://yellowstonesedgervpark.com/
We'll be there for 2+ weeks during the Memorial Day holiday timeframe.
GVP