To answer the original question, New York can be gorgeous weather-wise in September, but there's still the chance of a streak of brutal hot weather to trudge through. The edge of the summer heat, though, is gone by mid-September.
I actually prefer October, as by then it's decidedly cooler, but not as rainy as November can be.
I go married in NY in October. Perfect Day, Great Wedding..... the marriage... not so much!