the towels you rent are pretty good sized. like large bath towels. as far as cash. i recommend going into one of the gift shops (where you rent the towels ne ways so you will prob be in there to start) and get one of the mini gift cards with the ties. they can go around your wrist, or if you/your spouse/partner have a pair of board shorts with the elastic loop to put stuff around, you can just loop it through that. that's what i do. it stays in my pocket, and when we wanna use it i pull it out.
you can load it inside of the gift shop, and the cool thing is you can also use them at the parks. we do that because it helps control the spending on drinks and junk.