Clearly, you want to repair your roof at a time when it is not raining. For most areas in New York, this means mid-summer. But check the local weather forecast.
The best time to do roof repairs in New York is definitely late Spring or Summer. My father was a roofer for my uncle (his brother in law) who owns his own roofing company in NY where I'm from. They always worked during that time period.
Summer is the best time to do roof repairs in New York. You want the weather conditions to be optimal, to avoid accidents on the roof from ice or strong winds.