I've never been in September, but we tried April last year and loved it. Moderate crowds (over a week after Easter, but during some of the Northeast school breaks) and really lovely weather. It was hot, but not super hot or humid. It rained for about a half hour in the afternoon on a few days, but not all.

The week you're going is after the remaining few school breaks but at the beginning of the grad night season, I think. We had a few school groups touring in matching shirts, but they were fine and not a problem. Just plan ahead and take note of park hours. I think you'll find that it's a nice time to go.