Well, feel free to laugh at this...
I went with my cousin and we spent half a day at both Blizzard & Typhoon...I brought a very small back pack type bag with our sunscreen, a few dollars, room key, and an older camera I carried(that i wasn't worried about getting stolen). We got there early when it wasn't crowded and at both places we just stashed the dark colored bag in some bushes or greenery!! I realize this sounds ridiculous but it was completely hidden and it worked perfectly. We just threw our towls and shoes a few feet away in the sand or on the concrete and went on our merry way!! (just make sure not to forget where you stashed it!)