The FAA has the Hudson River and East River Exclusion zones Class B exclusion zones, in which VFR aircraft can operate. Considered together, they are known as a “Special Flight Rules Area”, or SFRA.
It extends in the north on the Hudson River to the Alpine Tower, then down to the Verrazano Narrows Bridge, and for the most part includes the entire river, shore to shore. It begins at 0 feet and extends to 999 feet for local operations. 1000- 1299 is for Transient aircraft. Above 1300 and you are in the Class-B NY airspace.
Part of the rules for operating here, and there are many, are two-way communications to self-report your location, heading and altitude. You must also have a current Terminal Area Chart for NYC. In addition, most of this area are close to many heliports scattered about, requiring normal notification procedures.
You can find a lot more information here:
Special Flight Rules in the Vicinity of New York City
And here:
https://www.faasafety.gov/files/gslac/library/documents/2010/Nov/48447/kneeboard.pdf
The entire South Side of the Verrazano Narrows is surrounded by part of Gateway National Recreation Area, and drone operations are prohibited.
From my perspective, and please do not take this as “legal advice”, but the only way to operate by the rules and fly near the Verrazano Bridge is the following:
· On the east side (Bay Ridge Brooklyn) Park in the small parking area off the Southbound Belt Parkway, just to the North of the Verrazono Bridge. The SFRA extends from the shoreline, you should take off as close to the shoreline as possible.
· Using two way communications, announce your location, altitude, direction of flight and intentions on a frequency of 123.05
· Stay below 400 feet AGL.
Good luck!