Back in 2002 we left NY in late Sept for Bermuda and then returned to NY around Oct. 5- if I remember correctly.
In Bermuda the days hit around 80 and lows of 60. We went swimming and it was warm enough.
I did notice though a definite chill that last morning in NY (low was around 40that morning) before we debarked. I was glad I was wearing slacks and had packed a jacket-I needed them in NY.