We have visited Yellowstone and Grand Teton many times over the years, but only once in September, back in 2007. That year there were forest fires somewhere in Idaho and the air in many parts of the Park smelled like a nearby campfire. Also the smoky haze made for poor photography. Also, we were surprised at the size of the crowds there at that time of year.
We much prefer to visit the Parks in late May and early June, when the chance of forest fires is much less and the crowds are smaller. We never make advance reservations for campsites and are usually successful either just showing up or calling ahead same day to two days ahead.
September is great if you want to hear the bull Elk bugling to attract the females.