Prepositions

He spends a few days in New York

Or

He spends a few days at New York.

What sentence is correct?

Both are correct but in this case, the first sentence is preferrable.  "in" means that he is inside the place.  "at" means around.  If you replace "New York" with "school", it means that he is PRECISELY inside a school building, implying that he may be in a class studying etc.  Using "at" means he is around the school area, could be just outside the school with implication of visiting, going etc.

preposition

He spend a few day in new York

Or

He spend a few day at new York.

What sentence is correct?

He spent few days (in) New York.