With thousands of miles of shoreline to establish a harbor at, why are places such as New York and Rotterdam fitter to harbor a harbor 
through which route maritime commerce? What natural features do they have that others don’t?
9 days to the most boring Super Bowl EVER.
Geographical location as opposed to other trading points is one thing. I´m not 100% clear on what you are asking though, “Why are NY and Amsterdam such well known and successful harbors” or “What is a natural harbor”.
A natural harbor is simply a strip of coast with adequately an adequately deep sea. OK, maybe that´s not a 100% clear.
What I mean is, that you can´t sail a ship onto a beach, because it gets gradually more shallow as you get closer to dry land. If you step over the edge of a natural harbor however, your feet don´t touch sand. You simply plummet deep into the sea, usually it´s because you´re actually standing on a submerged cliff. Such a spot is ideal to get a ship to land without grounding it on the shore.
Anyway, I hope I don´t sound patronizing or anything, I just had sort of a problem understanding my own line of thought. Haven´t had much sleep recently…
— G. Raven
If you want to look at the definition of the perfect natural harbor, look at a map of the San Francisco bay.
With such a narrow mouth (the Golden Gate) and huge area it is nearly immune to the heaviest open seas on the coastline.
IIRC, Rotterdam is a man-made harbor (Coldie?). Few, if any East coast harbors can hold a candle to the SF bay. It remains to this day one of the largest and finest natural harbors in the entire world.
New York is a successful harbor because it lies at the mouth of the Hudson River. I can’t comment on Rotterdam.
I knew I forgot something!
I believe some kind of enclosure is required, as mentioned in relation to the San Francisco bay, which is a good example. However I do not have command over the technical terms or knowledge of this aspect of the harbor phenomenon. 
I feel deeply ashamed, coming from a small fishing island that relied heavily on such harbors.
bows head in shame
Anyway, I´ll stop rambling on now…
— G. Raven
The world’s longest artificial breakwater turned the ports of Los Angeles and Long Beach into two of the world’s busiest. Without the breakwater, it was very difficult for ships to make it through all the sludgy stuff near the coast.
Rotterdam lies at the mouth of the Rhine river which travels through the heart of industrial Germany.Vessels suitable for the ocean are completely useless up the river so the lucky Dutch are employed unloading river boats and barges from Germany, and loading up ships of the world. Of course the reverse is applicable as well. The last time I checked, maybe 20 years ago, Rotterdam had just surpassed New York in annual tonnage.
Perhaps a translation from Japan would help, they know about harbors over there. Tsunami means harbor wave (so I have been told) in Japanese. I am a landlocked fool myself, but I would think the ideal harbor (natural or manmade) would provide a deep sea and adequate protection from all normal waves. You just gotta deal with the tsunami, nothing you can really do but try to live through those.
Alantus
The important things for a “Natural Harbor” are deep water near the shore, adequate access by land to the shore, and mild wind, wave and tide fluctuation. The last are provided by breakwater formation, and the shape, and orientation of the mouth of the harbor in relation to the direction from which the tide comes (East, here on Earth) The Islands of the Hudson estuary provide these factors admirably.
Economic factors play a greater role in the actual development of natural harborage into real life harbors. The long established infrastructure of the great harbors of history have sustained their success as technology has provided the means to improve the harborage in other location. While sailing ships needed the shelter of leeward anchorage for safety far more than a modern ocean going vessel, the modern vessel needs ready land transportation, and logistical support for markets in far greater volume than an entire fleet of sailing ships.
Once the port was in New York for half a century, other locations had a lot of catching up to do. The Hudson was navigable to sea going ships for a greater distance during the developing decades of the American colonies. That case is simply not a realistic issue in the modern world of shipping. But the rail, road, and air connections drawn to New York by the existence of the many harbors are a great advantage for those who dock there now.
Tris