Generally it is the precinct where they work. Some units work out of 1 Police Plaza.
The above answer, and any follow up comments or emails is for informational purposes only and not meant as legal advice.
You can serve them wherever you can locate them. However, you personally cannot serve it and your process server should already know how to do this.
If you are suing an individual -- any individual -- you always have the option of service at their residence, or anywhere the process server can find them -- in court, on the beat, wherever.
The NYPD is a city agency. Sue the city. Serve New York City Law Department. Name the officer and badge number as a Defendant in the complaint. Depending on the facts, the complaint may allege negligent hiring, assault/battery, negligence, false imprisonment, respondent superior, etc. The city will end up dolling out the money, anyway...
Retain an attorney on contingency agreement.
All responses to legal questions do not establish an attorney-client relationship.