"Snowless Joe's" is located near the entrance to the park. It is where you can rent lockers, or towels.
Lockers come in two sizes. The "Small" Locker costs $10/day, and the "Large" locker costs $12/day. These prices include a $5 refundable key deposit. I carried a "beach bag" with towels, shirts, sunscreen, and a couple of other odds and ends.
This easily fit in the "Small" locker without any problems. A tip about locker rental... Don't assume you have to take a locker next to Snowless Joe's.
The lockers there are right next to the changing rooms, and it is quite crowded (even on a slow day it was wall to wall people). Although you must get your locker key at Snowless Joe's, you can ask for a locker that is located in a different part of the park.
Towels are available at $2 per towel, but most hotels don't mind you bringing their towels with you, as long as you remember to return them.
Snowless Joe's Rentals also provides life vests free of charge to guests who wish to leave identification (passport, driver's license, other identification with photo or hotel identification).
Your own 'water wings' and float-belts are allowed, but anything beyond that is prohibited and enforced by the lifeguards present. (Side note: You can also bring eye goggles - especially if you have the custom type that take the place of glasses - but no face masks or fins.)
There are outside showers throughout the park and near the lockers. The only indoor showers are adjacent to the 'Snowless Joe's Locker Area.
Remember, it is never advisable to leave anything of value out in the open (or 'hidden' at your unattended sitting area) - even at Walt Disney World!
There are three locker locations in the park: "Snowless Joe's Locker Area," near the entrance on your right side; "Ski Patrol Locker Area," near that said play area for young children; and the "Double Dipper Locker Area," on the opposite, left side of Mt. Gushmore. All three can be rented at Snowless Joe's with a $5 refundable deposit. The regular lockers are $10 per day; the larger lockers are $12 per day.