While it's true that if you're having trouble with problematic neighbors, the landlord has responsibility to take corrective action, it isn't always quite that simple. There is a limit to a landlord's control over neighbors.
In addition, if you sue the landlord, you can become subject to blacklisting, and the consequences may be not be worth it. But what you can do is bring a private suit in New York State Supreme Court against the neighbors for being a nuisance. If you can prove that they are interfering with your quiet enjoyment of the property in a substantial way, and are acting in a manner that is intentional and unreasonable, you have the basis for a successful suit.
As a practical matter, you may find that a lawyer's letter threatening legal action does the trick in getting the villains to stop annoying you. Most people are afraid of getting embroiled in a lawsuit, and assume that it's likely to cost them a lot of money. So, consider starting with a lawyer's letter, and follow your attorney's advice from there.