Final answer:
The Sun is directly overhead at noon at the Tropic of Cancer and the Tropic of Capricorn on one day each year, at the Equator on two days each year, never in New York State, and never at the North Pole.
Step-by-step explanation:
At the Tropic of Cancer, the Sun may be directly overhead at noon on one day of the year, which is during the summer solstice on or about June 21. Similarly, at the Tropic of Capricorn, the Sun is directly overhead at noon on one day of the year, on or around December 21 or 22, which marks the beginning of the southern hemisphere summer.
At the Equator, the Sun is directly overhead at noon on two days each year: at the equinoxes, which occur approximately on March 21 and September 23. New York State (NYS), which lies well north of the Tropic of Cancer, never experiences the Sun directly overhead at noon throughout the year. The North Pole also does not have a day where the Sun is directly overhead; instead, it receives continuous daylight for 24 hours during the summer solstice.