Summer or winter, rain or shine, there's always great stuff going on in New York City, so there's no real "best" time to go.
Culture hounds might come in fall, winter, and early spring, when the theater and performing-arts seasons reach their heights. During summer, many of the top cultural institutions, especially Lincoln Center, offer free, alfresco entertainment. Those who want to see the biggest hits on Broadway usually have the best luck getting tickets in the slower months of January and February.
Gourmands might find it easiest to land the best tables during July and August, when New Yorkers escape the city on weekends. If you prefer to walk every city block to take in the sights, spring and fall usually offer the mildest and most pleasant weather.
New York is a nonstop holiday party from early December through the start of the New Year. Celebrations of the season abound in festive holiday windows and events like the lighting of the Rockefeller Center tree and the Radio City Christmas Spectacular -- not to mention those terrific seasonal sales that make New York a holiday shopping bonanza.
However, keep in mind that hotel prices go sky high, and the crowds are almost intolerable. If you'd rather have more of the city to yourself -- better chances at restaurant reservations and shows, easier access to museums and other attractions -- choose another time of year to visit.