When you submit the correct answer for a puzzle on the map, you get a message saying "Congratulations! You can now travel to the [directions]." This means that the current location is connected to adjacent locations in those directions. Conversely, there is a wall that stops you from moving to any of the directions not listed. The map wraps around on both top-bottom and left-right.
Once all the walls are found, the map looks like:
This spells out
NEEDLE POINT, the answer.