The idea I had for a fairy type gym might be better for a psychic type gym but I'm sure they can come up with a reason for it:
Essentially you go through what is implied to be your own brain and the puzzle is split into three parts. The first part has you follow a fake Hop through a large version of your house, it's basically like a game of hide and seek, find Hop three times, he battles you at the end and says something that's implied to either be how you feel or something he's said.
The second puzzle involves a chase with a fake Marnie down a seemingly endless road, during the chase word bubbles will pop up asking who she is, what her goal is, stuff like that. You finally stop where you first met Marnie and you both fight.
The final puzzle is a maze with a fake Bede at the end, he laughs at you the entire time. Find yourself at a dead end? He makes fun of your failure. Go down the right path? He'll try to convince you that you're going the wrong way. When you finally find him he's silent, when you beat him he calls you dumb and vanishes.