The academy’s location is a mystery, other than the fact that it is located in the Mountains of the Moon according to an article on Pottermore. According to this Wikipedia page, there are several locations for the Mountains of the Moon. Many Muggle geographers think that it is the source of the Nile River in East Africa. It is a legendary mountain range, which explains why the founders built the Academy out of the stone of the mountain.
The school itself is at least eight stories high, with the basement and sub levels just above sea level. This is to avoid flooding during horrible storms. Magic was used to extend the mountains enough to build a rainforest. The forest and the school’s castle is protected by elves and sprites. A thick mist envelopes the entire area in order to prevent non-magical people from discovering the Academy. Whenever a non-magical person comes across the mist, their memories of the castle are erased and they fall into a trance-like state. The trance stays with the person until they arrive back to their home, where they will fall into a deep sleep for a few hours. Once they awaken, the non-magical person will not remember seeing Uadagou Academy of Magic.