Each viewpoint listed above is worthwhile and has unique advantages and disadvantages.  The choice of which one to shoot from is obviously dependent on your own preferences. For photographic purposes, my preference is for viewpoints that don't impose a pane of glass between you and the view.  My favorite free (no cost) location is Brooklyn Bridge Park. Of the various non-free terrestrial options, I prefer as it allows good views of the Empire State Building and Central Park (the later only during daylight hours).

Below are various tips that are relevant to photographing NYC's skyline;

1. Tripods - In general, 24 hours a day, your photos will be sharper if you use a tripod.  After dark (or when there is little light), your exposure will require a longer shutter speed and the only way to guarantee a sharp picture is with a tripod.  An exception to this general rule is when you are shooting from a place which is moving and/or vibrating.  An example of this would be the Brooklyn Bridge which may be vibrating from the car traffic.

Most tripods have three legs and a center column.  The center column allows the camera to be higher than the height it would otherwise be if you used the three legs alone.  Unfortunately, use of the center column can compromise the rigidity of the camera's connection to the tripod's legs.  For this reason, conventional wisdom says to avoid using a raised center column if at all possible.

If carrying and/or using a full size tripod is not convenient then I recommend a mini-tripod as almost any tripod will result in a sharper image when shutter speeds are long. The author has found the Gorillapod line of mini tripods to be very compact, light and versatile when traveling light. Full size tripods are generally not allowed at the paid locations listed above but I have found that mini-tripods (such as the Gorillapod just mentioned) are ignored.
2. Use a Self Timer or a Remote / Cable Release (this section assumes the use of a tripod) - The movement of your finger in pressing the shutter release can easily move and/or send small vibrations to your camera and result in a blurred image particularly if you are using a long shutter speed. This can happen even if your camera is mounted on a tripod.  There are two easy solutions for this. 

The use of a Remote / Cable Release will allow you to release your camera's shutter without actually touching your camera.  There are wired cable releases and there are wireless shutter releases. There are even app's that allow one to use their smartphone wirelessly as a shutter release. 

Another approach is to use your camera's self timer.  Using a self timer will allow the image to be captured a few seconds after you have fully removed your hands / fingers from the camera.

3. Avoid Mirror Slap (for DSLR users) (this section assumes the use of a tripod) - If you are using a DSLR then the movement of the mirror, the "slap" of it when getting out of the way as an image is actually captured, causes a vibration that has the potential to blur an image.  Some cameras have a mode (check your camera's menu of options) specifically designed to address this issue that will instruct the camera to move the mirror out of the way a few seconds before the shutter is opened to capture an image.  These few seconds will allow any vibration caused by mirror slap to dissipate.  On many Nikon DSLR's the menu option is called "Exposure Delay Mode" (I am not sure what this may be called on other manufacturer's cameras).

In real life situations a camera is more likely to have an image blur from being handheld than from mirror slap so your first priority should be to use a tripod or to set your camera down on a stationery object and only then worry about mirror slap. The issue of mirror slap is generally much more pronounced at long shutter speeds than at short shutter speeds.

4. Composition+ - There are "rules" of composition and there are times when one should ignore some or all of these same rules. In fact, there really are no rules in the formal sense, just ideas about composition that over time have become accepted as such although it is also accepted that they don't always apply. If you are shooting for yourself then you are the "client" and therefore you are the final judge of your images and its composition.  Having said that, here are a few (unoriginal) thoughts about composition and other related topics that I hope will be useful.

 
Near - Middle - Far:
Conventional still photography creates two dimensional images of what are in real life three dimensional objects. One way to convey this three dimensionality in a two dimensional image is through the use of elements in the images are near, middle and far.  The viewer of the image will generally move their gaze through an image going from objects that are near to those that are far.  A classic example of this might be an image with flowers or rocks in front of a lake with trees or mountains at the far end of the lake. The viewer's eyes will move through the image from the objects that are nearby to the objects that are far away.

Rule of Thirds: Imagine dividing an image with two evenly spaced horizontal lines and two evenly spaced vertical lines (sort of like a Tick-Tack-Toe board). A classic principle of composition states that placing an object (i.e. the main object of an image) where these lines intersect will naturally draw the viewer's attention to this object.

Light / Dark: If an image is dark with one bright spot then one can easily imagine that a viewer's eyes will be drawn to this light spot.  Similarly, if there is a distracting light colored object in your image then it can draw your viewer's eyes away from what you want to be the main object(s) in the image.

Contrast: Similar to Light / Dark (above), our eyes are naturally drawn to high contrast objects in an image. 

Edge Patrol: Carefully check the edges of your image for any objects jutting into the frame or that are otherwise distracting that may draw a viewer's attention away from the object(s) you want them to look at.

Crop in Camera: If an object is in your frame but is irrelevant to your composition then zoom in, reframe or move to eliminate it. A truly irrelevant object can easily distract from your composition.


5. - Helicopters vibrate.  Leaning your camera against a window or bracing it against some other object in a helicopter will allow the vibrations of the helicopter to vibrate your camera and thereby possibly blur any images that it captures.

It is recommended that you use the fastest shutter speed that you can given the ISO and other settings and to engage any image stabilization / vibration reduction mode your camera or lens might have. Some cameras / lenses have two IS / VR modes, one for typical situations and a more aggressive one for when there is movement in all directions.  In a helicopter use the most aggressive IS / VR mode offered by your camera / lens.

If at all possible it is preferable not to have to shoot through a pane of glass or plastic. Some helicopters might have an operable window and/or the option of removing a door.  If this is possible then the first and most important thing to remember is safety both for yourself and for those below if you drop anything. There is a tremendously strong wind generated by the helicopter's rotors immediately outside of a helicopter.  Make sure that that you are yourself properly strapped in and that your camera is firmly attached to you or an object that is firmly attached to the interior of the helicopter. Do not use detachable lens hoods as the wind might blow them off. Secure lens caps and any other loose objects inside a securely closed (zippered, buttoned etc) pocket before take-off.

If you are using more than one lens then it is probably much more efficient and safer to have a multiple of bodies (probably no more than two) with you than to have to switch lenses mid-flight (especially if the door has been removed. Changing lenses is also likely to be costly given the cost of flying in a helicopter with the wasted time spent changing lenses. For similar reasons, the use of a zoom lens is recommended as it is more versatile than the use of prime lenses. 

If the door has been removed then there should be no loose / unsecured objects in the helicopter. A BlackRapid Double strap can easily secure two cameras to yourself. Make sure that the attachment from your strap / harness to your cameras has been tightened / secured prior to liftoff. It is not recommended that you rely on typical camera straps as they can slip off one's shoulder or out of one's grip accidently. Do not change lenses on a camera during the flight and make sure that any lens caps and lens hoods have been removed and put into a secure (locked, zippered or buttoned) closed compartment / pocket. There should be no unsecured / loose objects in your possession during the flight.

Two cameras, each with one zoom lens, can probably cover any photographic situation you will face in a helicopter.  While a "super zoom" (a zoom lens with a very wide range of focal lengths) might be very versatile and lower in cost, the use of narrower range zoom lenses will generally result in better image quality and the option to use faster lenses.  As an example, I recommend the use of a 24-70/2.8 and a 70-200/2.8 (on a full frame DSLR).  Alternatively, the use of f/4.0 lenses can also be a worthwhile as long as you are shooting during the day when the speed of the lens is not a paramount issue.

Depth-of-Field (DOF) is generally not a problem when shooting from a helicopter as all of the subjects in your frame are likely to be at infinity or close to it.  Since the subjects of your image are all likely to be at infinity or very close to it, one generally does not need to use a small aperture to gain maximal DOF. As most lenses are sharpest two to three stops smaller than their largest possible aperture, there is no advantage in stopping down any further (especially since you want to use the fastest possible shutter speed to offset the helicopter's vibration).

When shooting at dusk or at night the use of cameras with above average high ISO performance (i.e. Nikon D5) and faster lenses (f/2.8 or faster) with built-in vibration reduction / image stabilization are highly recommended.

Camera meters usually assume that the world reflects 18% of all light (as does a gray card). This is why a picture with a lot of snow or light sand in it may appear darker than it does in reality or why a photo of a dark object may result in the object appearing lighter than it really is. At dusk or later setting a camera's exposure compensation is usually required to have dark areas of an image appear dark.  Exposure compensation varying from -1 to as much as -3 EV (exposure value) may be necessary to have dark areas of an image appear dark when shooting at dusk / night.

There is an obvious friction at dusk / night between getting images of the highest quality and getting sharp images. If the goal is to get an image showing a blur then you can skip the rest of this paragraph as you can use slower shutter speeds. The use of faster shutter speeds that are needed for sharp images will be traded off against the methods used to get that faster shutter speed. Trade-offs, which will lower image quality, include using a higher ISO setting and setting lens apertures to their widest setting. The author has used ISO's as high as 16,000. The specific combinations of high ISO setting, the use of at or near maximum f-stops and metering with minus exposure compensation is up to each photographer.

Lighting conditions change quickly at dusk and helicopter time is not cheap. The use of Aperture Priority metering is recommended to best deal with this. The use of manual metering means that you will spend more time manually changing your settings. The use of Shutter Priority would force the constant manual changing of shutter speed as the amount of light changes. The use of Aperture Priority means that the fastest shutter speed will always be automatically used based upon the aperture you select.

With metering set to Aperture Priority the camera settings that will need to be changed as the sky darkens will be ISO and exposure compensation. Experimentation, experience, looking at histograms on the camera's LCD (expect a skew to the left as the image will be mostly of darker objects) as well as looking at images on the LCD during your flight will help guide you when changing ISO and exposure compensation.