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From the Wikipedia page for New York City:

New York – referred to as New York City or the City of New York to distinguish it from the State of New York, of which it is a part – is the most populous city in the United States and the center of the New York metropolitan area, the premier gateway for legal immigration to the United States[6][7][8] and one of the most populous urban agglomerations in the world.

Does it simply means premier place? I know the meaning of both words separately but I am not sure about the combined meaning that I interpret.

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Short answer: Yes, that is what it means.

In the context, it means that more legal immigrants arrive through this city than any other.

In general, this description will try to imply that somewhere / something is the best of its kind; but overuse by advertisers tends to make it sound as if it may only be top of the list in some obscure respect - as in this case, to some extent. If it's being used by an independent commentator it's more likely to be trustworthy, although it isn't something I'd commonly use in natural speech anyway. See it & suspect a sales pitch!

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