The point closest to the Earth's centre (~6353 km) is probably somewhere at the bottom of the Arctic Ocean (depth ~4 km) near the Geographic North Pole (the bottom of the Mariana Trench is 6366.4 km from the centre of the Earth).
The lowest point on dry land is the shore of the Dead Sea, 418 m below sea level.
But the earth is oblate due to its rotation and lunar effect, so the poles are closer to the centre than anywhere on the equator ... ... by about 20 km.