Why did New York become the financial hub of America, rather than one of the other big cities?
There are several reasons:
New York was a natural trade center for a few key reasons.
Access to Upstate NY
Upstate NY was very important place in commercial history. The settlement of New York was driven by access to beaver and other furs, and the Hudson River was the 16th century equivalent to an interstate highway, leading right to the port of New York City.
Later, as fertile land in New England was accounted for, agriculture became a huge force. The feudal-style Dutch Patroonships produced all sorts of goods, and the Schoharie Valley was called "the breadbasket of the american revolution", and much of the agricultural surplus was shipped down the river to New York. Later, the construction of turnpikes opened up the interior of Central NY, which meant more farming, more credit & banking activity in Albany and NYC and more economic activity.
Most of the English Colonies were formed by relatively homogeneous, religiously-oriented communities. New Amsterdam was totally different -- it was a commercial venture of the Dutch West India Company. Being motivated by money vs. god, there was a diversity of religious backgrounds, languages, etc.
The Erie Canal
The construction of the Erie Canal brought New York to a whole new level -- the flow of goods from Western New York and Ohio all came through New York to be shipped all over the world.
All of this stuff created a scenario where New York City became this dense concentration point or hub for wealth and trade. Until the later half of the 20th century, this proximity made the New York metro region a premier industrial center -- which further strengthened it's role as a financial center.
I would add that Holland was the financial centre of the Earth in 17-18th centuries. NY, having the best specialists in finances simply couldn't fail.