If you're interested in the factors that drive a city to be founded, grow, and prosper, you might be interested in Edward Glaeser's Triumph of the City. Glaeser, a Harvard economist, examines economics, policy, history, and factor endowments in order to examine what makes cities prosper (and decline). While Triumph of the City is a prescriptive anthology, examining case studies on individual issues impacting various cities around the world with conclusions offering policy recommendations, both New York and Boston are mentioned extensively. The author even admits an affinity for the two places: New York is Glaeser's hometown, while Boston is where he built his career (in addition to teaching at Harvard, Glaeser is a fellow at the Rappaport Institute for Greater Boston) explaining why both cities are granted special attention.

Glaeser identifies two factors unique to New York which contributed to it surpassing Boston in economic importance. While both factors have largely to do with factor endowments, only one is a true natural advantage: the size and depth of New York Harbor. Along the entire length of Manhattan, and farther up until around the Tappan Zee, the Hudson River is "downed;" amounting to a very deep saltwater inlet not dissimilar to a fjord (without the characteristic mountains). Vitally, this means New York's harbor could shelter larger steam-powered ships, while Boston couldn't. In later decades, both Boston and New York would use landfill to free up valuable waterfront real estate, however shipping traffic in the much larger New York harbor could more easily migrate to equally convenient deepwater docks nearby, first from Manhattan to Brooklyn, and later to Newark.

So the depth of New York's harbor already makes it a natural entrepôt for goods to be unloaded from large oceangoing ships onto smaller vessels destined for the minor ports of the United States and North America. But the city's second advantage, this time facilitated by geography rather than entirely derivative of it, was also determinant: the Erie Canal. The Erie Canal, connecting Lake Erie to the Hudson River, turned New York into the natural outlet to globally ship raw materials and finished goods extracted and produced in and around the Great Lakes. It cannot be understated how important the Great Lakes were to the creation of an industrial macro-economy in the United States: the lakes facilitated he transport of iron mined in Minnesota to factories in Chicago, Cleveland, Detroit, and even New York, where machinery, goods, and appliances were produced fueled by engines powered by coal extracted in Pennsylvania, also shipped along the Great Lakes. So these materials and goods alike were shipped through Lake Erie, across the canal, and down the Hudson River to New York City. Boston, on the other hand, had no such connection.

One of the major factors which determines a settlement's rapid growth is its status as an entrepôt: a place where goods can and must be moved from one mode of transport to another. Where goods already need to be unloaded entrepreneurs find it convenient to to build factories, so they can be transported straight to their destination. New York proved to be North America's most convenient entrepôt. That's not to say Boston isn't a successful city in its own way: Glaeser points out that the city has become one of the world's foremost centers of innovation and professional services. Boston is, after all, one of America's oldest cities; long before it was eclipsed in importance, North America's oldest and most prestigious universities, insurance companies, and law firms already took root. This university professors offering to consult for companies could morph into consulting firms, university laboratories begat research centers, and so on and so forth.

u/MrDowntown and u/lord_mayor_of-reddit might be able to also offer more insights into New York's more rapid growth compared to Boston, as well as to answer your more specific questions tied to the rollout of a grid system.