The city runs through four very different seasons, and the right month for you depends on whether you plan to walk or to sit indoors.
Autumn
Autumn gives the best walking weather of the year. September starts warm, with highs in the mid-70s Fahrenheit, which is about 24 Celsius, and cools toward the mid-50s, about 13 Celsius, by November, while the humidity drops away. Central Park and Prospect Park turn red, orange and gold, and the calendar fills up: the New York Film Festival, the new Broadway season, the Village Halloween Parade, the TCS New York City Marathon, which runs across all five boroughs, and the Macy's Thanksgiving Day Parade at the end of November.
Winter
Winter is cold and quiet. From December through February the average high sits in the high 30s to low 40s Fahrenheit, which is roughly 3 to 5 Celsius, nights drop below freezing, and the season brings 2 to 3 feet of snow, though the total swings a lot from year to year. This is the stretch to use for the museums: January and February are when you can see The Met and MoMA without working through a crowd. December carries the holiday lights of Dyker Heights, the Rockefeller Center Christmas tree, the Radio City Christmas Spectacular, and skating at Rockefeller Center or Bryant Park's Winter Village.
Spring
Spring arrives slowly and brings the rain with it. March holds highs near 50 Fahrenheit, about 10 Celsius, and May reaches the low 70s, about 22 Celsius, so pack an umbrella and a jacket you can carry. The cherry blossoms at the Brooklyn Botanic Garden and in Central Park are the season's main event, joined by the Macy's Flower Show, the Tribeca Film Festival and the St. Patrick's Day Parade. Once the warm weekends start, Smorgasburg reopens and the High Line and the walk across the Brooklyn Bridge become the natural afternoon.
Summer
Summer is hot and humid, with average highs in the 80s Fahrenheit, roughly 27 to 30 Celsius, from June to August. July is the warmest month, and brief heavy thunderstorms in the late afternoon are part of the routine rather than a surprise. Evenings carry the Fourth of July fireworks, free Shakespeare in the Park performances and the SummerStage festival in Central Park. When the heat gets to you, the ferry to the Statue of Liberty and Ellis Island, an air-conditioned museum, a classic baseball game or the beach at Coney Island all work as a plan B.