Final answer:
The location in the question is the North Pole since moving 1 km south, 1 km east, and 1 km north from there leads you back to the starting point, utilizing the Earth's circumference near the pole.
Step-by-step explanation:
The scenario described in the question is a classic illustration of a specific location on Earth known for having these properties: the North Pole. If you start at the North Pole and move 1 km south, then 1 km east (which would be a circular path around the pole), and then 1 km north, you will indeed end up where you began. The circumference of the Earth near the poles allows for such a path to exist, as moving eastward after moving south from the North Pole creates a loop that leads right back to it. Another possible but less well-known set of locations would be near the South Pole on some specific circles of latitude, where a similar but far more complex set of paths could be taken to end up at the starting point due to the way circles of latitude shrink closer to the poles.