As mentioned, yes there are fireworks in CP - here is a blurb from a website I came across when I GOOGLED 'fireworks-central park':
In New York City, New Year's Eve is celebrated with vigour as the traditional midnight fireworks are let off in Central Park, South St Seaport and Prospect Park in Brooklyn.
Spectacular in its own right, New York City has masses to offer during the New Year celebrations. Those looking for sheer numbers should head for Times Square to see the famous ball drop at midnight. But, if you don't fancy freezing on the street with tens of thousands of people, we recommend you book to go to a restaurant or bar close to one of the firework locations and aim to finish in time to catch the pyrotechnics.
Uptowners should head for Central Park, where the explosions signal the start of the New York Road Runners Midnight Run, Brooklynites for Prospect Park and those hankering for stunning cityscape views should definitely go for South St Seaport. With its location on the East River and close to Brooklyn Bridge, the views are awesome.
Hope this helps!