New Scientist has an article and a series of maps on the subject of "the most remote place on earth." They make their determination based on "how long it would take to travel to the nearest city of 50,000 or more people by land or water."
Embedded above are maps of the worlds roads (top) and navigable rivers (middle). Based on these data plus ocean shipping routes, they have determined that less than 10% of the world is more than 48 hours from a major metropolis, and that a spot in the Tibetan plateau (bottom) is the most remote, because it is a three-week trip to Lhasa (1 day by car and 20 days on foot).
But, in terms of being the farthest distance from people in any direction, the most remote spot on earth I think is HERE. The coordinates are -40.349679, -9.880598. It doesn't look very impressive on the initial click, but as you zoom out you see first the volcano, and then the incredible isolation.
It's Tristan da Cunha, a dependency of St. Helena. Their website is here, and a Reddit discussion is here.