Where in the spinning cycle is there the most potential energy?

In the spinning cycle, any fixed point on the wheel goes through a cycle. It goes through a point of maximum elevation and point of minimum elevation. The minimum elevation point is typically the ground surface, if you are cycling outdoors. Since the potential energy is a function of the height of an object with respect to a datum, the maximum potential energy is at the highest point in the cycle. This point is at the greatest distance from the ground. 

A point from its location of maximum potential energy goes to the lowest point, a position that will correspond to minimum potential energy. During this motion, the potential energy converts to kinetic energy. Then the point again goes towards the maximum elevation and energy again converts to potential energy. 

This energy conversion continues as the cycle spins.

Hope this helps.