Is there anything in the Coliseum?
According to this article, the whole point of the coliseum is to get the weapons of the strong enemies within it:
The whole gimmick to this area is that it's full of the most powerful enemies relative to where you are in the game, and each of them is wielding rare weapons for you to take once you've disposed of them.
Most importantly, every single enemy has some kind of elemental weapon. Flameblades, thunderblades and frostspears are plentiful in the coliseum.
From what I've read, the strongest enemies in the game (excluding bosses) are within the coliseum, making it a challenge to get their weapons. There are also two treasure chest at the top of the ruins.
There is also a Korok on a ledge beneath a chest above the entrance and under a rock