There aren't a lot of great things to say about New York City weather. There are distinct seasons, which is a plus, but it seems like summer and winter are always a whole lot longer than spring and fall.
During the summer, it is often hot and humid, but thankfully even the hottest days rarely break 100º F. The hottest month is July, during which the average high temperature is 85º F. It's not hot enough to make you melt, but certainly hot enough to warrant a window A/C unit or strong fan. Spring and summer can be a little bit wet, with about four inches of rain per month, but there are sure to be some dry and sunny days mixed in.
The winters are a lot like the summers, cold, but rarely extremely cold. It will only get below 0º F once every couple of years. Although winter snow is a bit unpredictable, New Yorkers will face the occasional Nor'easter. In 2010, for example, New York City was blasted by 20 inches of snow during the holidays, which crippled the city for days and changed quite a few holiday plans. Even if it's not too snowy, is going to be chilly and windy and between walks to the subway and waiting for the bus, you'll probably be spending more time outdoors. A hat and gloves are a must on most winter days!
Fall and spring are wonderful in New York. The spring can be rainy, but expect mild temperatures in April, May, September and October. After the long hot summer or icy winter, spring and fall seem just about perfect.
Your best bet for living in New York City is to expect quite a bit of variety from the weather. During the summer and winter, expect it to get very hot and cold, respectively, with a little bit of rain and snow mixed in. Make sure you have a warm winter coat, sturdy umbrella, and a nice pair of boots and you will be all set for anything the city can throw at you.