We went the first full week of September one year. It was the best crowd wise in all the times I've been there. For many schools, this is the first week back so many people don't take their children out of school that early in the year. We walked on to just about everything. In fact, until the weekend, they didn't even uncover the fast pass machines! We absolutely loved that part of the trip. The only downside was that it was still very hot and humid. Because of that, we went the next year at the end of October. There were more crowds (although not "summer" crowds) and it was a bit cooler.
If you don't mind the heat, that first week in September was great!