I've only been once, so I'm probably not the best person to ask. That said, visiting in early September worked out really well for me. I got fantastic colors and saw a ton of wildlife, from caribou (see the image in my other comment), to moose, and even a lynx.

The only downside is that the weather can be a bit gross at that time. It was below freezing at night and rained every day of my trip. I was fine with camping in that weather, but it might be an issue for some people. The advantage of the weather is that it keeps the crowds considerably smaller than at peak.