I spent every summer as a child 60+ years ago in Yellowstone NP. My cousins worked in the park and I would stay with them as they worked. I recommend getting started early in the day to avoid the crowds. . . it seems that foreign tourists will occupy the RV parking spots without concern for the spots that they occupy. . . it can get competitive.
Which entrance you use is not as important as where you visit. The Hayden Valley is a must. . . talk to the rangers and ask for their input. They've sent us to amazing uncrowded locations without tourists that we hiked into. They actually said to hike to remote thermal pools and said to walk to edge of the pools if there were bison tracks surrounding the pools.