As others have noted…either before school lets out or after it starts again. 10 years ago that was excellent advice…but the last time we were there in 2019 while it was less crowded in September it was a lot more crowded than the times before in 2013 and 2016…and there was a lot more road construction. I would still go…but like many other parks we found that arrival at sunrise, spend 3-4 hours and head back to the campground before the crowds built up really kept the crowds down and we got better light as well. But…in 2019 we were camped west of West Yellowstone and got to the entrance before sunrise…50 cars backed up and it was almost bumper to bumper traffic on the road in from West Yellowstone along the river…and this was at 6:30 in the morning in late September…but we just stopped in the road along with 500 of our closest friends and got some great shots of a bull elk crossing the river with golden hour light on him…although we didn’t stop for any reason other than we had no choice…cars were stopped as far as we could see ahead of us because of the elk.