If you’re talking about New York City in general, the answer is a bit more nuanced than just naming one station, but yeah, most intercity trains arrive at Penn Station (Pennsylvania Station) in Manhattan. It’s basically the main rail hub of NYC and handles Amtrak, NJ Transit, and Long Island Rail Road, so if you’re coming from another city or state, there’s a very high chance you’ll land there.
That said, not all trains go to Penn. For example, Metro-North trains (coming from places like upstate New York or Connecticut) usually arrive at Grand Central Terminal, which is another major station but serves a different network.
Also, Penn Station is more functional (crowded, busy, a bit chaotic), while Grand Central is more organized and visually iconic. So yeah, it depends on your route, but if you had to pick one default arrival station, it’s definitely Penn Station.
Penn Station is the primary arrival hub for most intercity trains into NYC.