Not every immigrant into the United States filtered through New York City. Many did, but there were other ports of entry–both on the west and east coasts of the United States. There were immigrants who originally landed in Canada and crossed the border into the United States. My own forebears landed in New York, Baltimore, and New Orleans and one pair originally came to New Brunswick and crossed into the United States a few years later.
The initial point of arrival could have been impacted by the final destination within the United States. Most of my 19th century immigrants knew where they were headed: the rural upper Midwest. That impacted where they arrived.
You may have to get New York City out of your head to find your immigrant’s manifest entry.