New York City very much has a four season climate, but there's a lot of variability from day to day. Fall can often be beautiful here, sunny and relatively warm days with nicely cool nights. It's a very invigorating time, although the days are shortening, which anyone who gets up early notices since NYC is towards the east end of the time zone. Fall days can also be wet and cool. Humidity goes up and down a lot, and high humidity makes heat hotter and cold colder. Wind tends to be magnified in Manhattan because so many blocks are lined with tall buildings that channel the wind, so a wet, windy, cool day in the fall can be very uncomfortable. A lot of New Yorkers love their street life, so if it's anywhere near warm enough they'll be sitting in out door cafes enjoying the day even if they have to be in jackets or coats. While we do see snow in winter, we generally see very little of it until after the New Year, although there are exceptions. As fall goes on, days and nights gradually get cooler. To give you some idea of variability, I have been to the Macy's Thanksgiving Day Parade dozens of times (I live near where it begins). I have watched it in all kinds of weather, from in the 20s with light snow to sunny and the 60s. Today the predicted high is 77, although the average for the date is about 68. The record high is over 80. The predicted low is 61, although the average is about 55, and the record is about 36. The weather statistics are very easy to find on the web. If your story is set in a definite year or years, simply look up the weather for the time you've picked.
Fall by the way is when everything changes in NYC. The schools go back into session. Baseball is winding down, and the Yankees are usually in the play offs. Football and then hockey and basketball begin. (We've got 11 major league sports teams, 2 baseball, 2 football, 2 basketball, 3 hockey and 2 soccer.) This is not a big college football town but there is a lot of attention paid to college basketball. The new Broadway season begins in September, so by later in the fall discussion is about which new shows are going to make it and which won't. All the TV networks are headquartered here, so there is a lot of talk about the new TV seasons, too. Towards the end of the year, Oscar discussion picks up as the last big blockbusters open for the Christmas season. Most years are some sort of election year since the city elections are in odd numbered years while the federal and state elections are in even numbered years. The Christmas season is huge here. Stores decorate beyond belief, and people come from all over the world just to see the store windows. The sidewalks on Fifth Avenue, the main shopping street, become nearly impassable. Lord & Taylor's windows are so popular that you have to wait in line to see them. The city is very full with tourists from Thanksgiving until New Year's. The lighting of the tree at Rockefeller Center just after Thanksgiving is a landmark day every year. On December Saturdays, Herald Square, where Macy's is, is the busiest passenger intersection in the world. Vehicular traffic during the season is also horrendous. Once you get past Thanksgiving, there is an incredible number of holiday parties by employers and organizations and individuals. And then there is of course Times Square for New Year's eve. By the time you get to January, there is a sense that the whole city is near exhausted.