Antarctica doesn't have traditional "coasts" like other continents. It's a massive ice sheet with the South Pole located near the center of the landmass. So, there isn't a coast that's closer to the South Pole than any other.

However, the Transantarctic Mountains, which run across the continent, are closest to the South Pole. These mountains roughly divide the continent into two parts. The Queen Maud Land and Wilkes Land regions are closest to the South Pole, with the South Pole itself being located on the high plateau of East Antarctica.