What point of the earth is closest to the moon?
At any time, the closest point is on the line joining the centers of the Earth and the moon. If you ever see moon right above your head, you are closest then. There are limitations for latitude.
Assumption; Earth is a sphere. The point on a sphere nearest to an outside point is on the radial line, from the center to the external point. The moon's orbital plane is inclined to the ecliptic ( the Earth's orbital plane) at 5.145 deg, nearly. Our equator is inclined to the ecliptic at 23.4 deg, nearly. So the locus of the point closest to the moon is a great circle touching latitude circles 28.5 deg N and 28.5 deg S, nearly. It really becomes a project, for spheroidal Earth. Anyway, it is a good question. I mean 'What point of Earth ...?'.