The seasons don't really start to change drastically until November. That's when the big North Atlantic high that rules during the summer starts to move south after doing battle with the northern air masses which move down and give us more NW/N components. Catching the back end of these northern high pressure systems is a good thing if you're headed down the coast.
During Sept., the major threat is tropical storms which historically peak in Sept. and then fall off sharply toward the middle of October. Going south, the best window is when this transition takes place. It can vary significantly from year to year. Watching the 500mb(upper level) NOAA chart patterns is a good clue as to when the seasons are actually changing. If you can catch the back end of a big N/NW high in Sept., it will give you a run or reach all the way NE up the Sound. Don't go if there is any chance of a low following right behind the high. If you catch the high too late, it can also mean motoring in flat conditions. Once a big high settles in, it can mean 0 wind for a long period because by Sept. some of the summer SW onshore breezes have diminished.
I always watch for the type of clouds to determine where a northern high is in its cycle. When small, broken, sharp, black batches of clouds start to appear on the horizon, scudding across the sky, it's a signal that the wind is going to blow HARD from the N/NW at the start of a northern front passing through- not the time you want to be out unless you want to practice your survival sailing techniques
If you're going the Sound route, you might want to just stay inside and anchor up at Fisher's Island the second night and then go up Fishers Sound past Watch Hill and on to Newport. Day 1- NYC to PJ, Day 2- PJ to Fisher's, Day 3 Fisher's to Newport. Once in Newport, you can make the GREAT sail out of Narragansett over to Block and back.