Using Hudson St and 6th Avenue for a reference point, an explanation of the airspace and altitude restrictions: The airspace over that portion of Manhattan is what is called Class Bravo, formerly know as a Terminal Control Area (TCA). It extends from the surface to 7,000 feet. Within this airspace all aircraft are under positive control of ATC (Air Traffic Control). I don't know the minimum vectoring altitude (the lowest altitude a controller can assign an aircraft when directly assigning altitude and heading) since it is not published on navcharts, but in a book called the TERPS which is the procedural guide for controllers. The Federal Aviation Regulations on this subject are as follows;
§91.177 Minimum altitudes for IFR operations.
(Note: all major carriers operate IFR)
(a) Operation of aircraft at minimum altitudes. Except when necessary for takeoff or landing, no person may operate an aircraft under IFR below --
(1) The applicable minimum altitudes prescribed in parts 95 and 97 of this chapter; or
(2) If no applicable minimum altitude is prescribed in those parts --
(i) In the case of operations over an area designated as a mountainous area in part 95, an altitude of 2,000 feet above the highest obstacle within a horizontal distance of 4 nautical miles from the course to be flown; or
(ii) In any other case, an altitude of 1,000 feet above the highest obstacle within a horizontal distance of 4 nautical miles from the course to be flown.
However, if both a MEA and a MOCA are prescribed for a particular route or route segment, a person may operate an aircraft below the MEA down to, but not below, the MOCA, when within 22 nautical miles of the VOR concerned (based on the pilot's reasonable estimate of that distance).
(b) Climb. Climb to a higher minimum IFR altitude shall begin immediately after passing the point beyond which that minimum altitude applies, except that when ground obstructions intervene, the point beyond which that higher minimum altitude applies shall be crossed at or above the applicable MCA.
§91.119 Minimum safe altitudes: General.
Note: This applies to IFR and VFR operations, meaning everyone)
Except when necessary for takeoff or landing, no person may operate an aircraft below the following altitudes:
(a) Anywhere. An altitude allowing, if a power unit fails, an emergency landing without undue hazard to persons or property on the surface.
(b) Over congested areas. Over any congested area of a city, town, or settlement, or over any open air assembly of persons, an altitude of 1,000 feet above the highest obstacle within a horizontal radius of 2,000 feet of the aircraft.
(c) Over other than congested areas. An altitude of 500 feet above the surface, except over open water or sparsely populated areas. In those cases, the aircraft may not be operated closer than 500 feet to any person, vessel, vehicle, or structure.
(d) Helicopters. Helicopters may be operated at less than the minimums prescribed in paragraph (b) or (c) of this section if the operation is conducted without hazard to persons or property on the surface. In addition, each person operating a helicopter shall comply with any routes or altitudes specifically prescribed for helicopters by the Administrator.
Hope this helps!
DD