Along with all the previous answers cheap thrills usually has jet skis. Make sure to call ahead with any of these to scheduke a time because they book up fairly fast.
There are a few places to rent the jet skis , in town right before entering the park
There is a shop on the Main Street "55" before you turn left on the Payette lake. They do rent or have all outdoors sports equipment that you can choose. I am pretty sure that they have jet skis to rent.
McCall sports in downtown McCall.
Try the Mile High Marina in McCall
Try the marina downtown, you would likely have to drive there though.
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