The history of New York is inextricably tied to the oyster. Oysters were harvested by the first settlers of the region, the Laganape tribe and were coveted by the Dutch settlers (although they were disappointed to find that New York oysters contained no pearls. During the 19th century, New York harbor was the largest source of oysters worldwide. At that time oysters were cheap and primarily eaten by the working class. The oysters in New York were one of the primary foundations for the city's still dominant restaurant trade. Eventually the wild oyster population was depleted and farming began in the harbor. Farming brought disease into some of the beds and oysters became more scarce, driving up prices and catapulting them into the luxury realm. Pollution from the rapidly expanding New York population eventually made the oysters in the New York Harbor inedible, effectively halting the city's trade completely when the final oyster bed was closed in 1927. There have been on-going efforts to clean up the harbor enough to make the oysters edible, but any actual results are still many years in coming, but conservationists are hopeful.
Once the Hudson Estuary contained 350 square miles of oyster beds and it is estimated that over half of the world's oyster population was in the New York Harbor. If that doesn't give you a picture of how big the oyster industry was in New York in the late 1800s, consider this. In 1860 12 million oysters were sold in local markets. By the 1880s 700 million oysters were harvested in the New York Harbor (these numbers come from the New York Times, so I'm assuming they are accurate.) Before pizza, before bagels, before dirty water hotdogs and pretzels, oysters were New York's most iconic street food. Oyster cellars were everywhere, especially near the Fulton Market, the Seaport, and in the Five Points neighborhood. The most famous of the early oyster cellars was Downing's which opened on the corner of Wall and Broad Streets in the early 1800s. The first elevated oyster bar was probably Delmonico's which popularized serving oysters on the half shell.
For more oyster reads (aka the sources where all of this is paraphrased from) check out the articlesHistory on the Half-Shell andThe Mollusk That Made Manhattan. Another great resource is the New York Public LIbrary's digitized menu archive. With a little searching you can find menus from a few old oyster houses as well as some long-gone Bowery Restaurants.