In our old rig we used command hooks, in our new rig we use an over the door type.
Dick, Joyce, Diego, Picatso and Gustav
2017 3720 RL, and 2013 HC 343RL
2017 3500 Dodge Maxi DRW 4X4, Pullrite Hitch, IS, Disk Brakes, 3rd AC, Winegard Traveler, Bathroom door mod, Dometic 320, couch for desk swap, etc.
As a 3582 owner, here's another option, a freestanding electric towel warmer. Stands next to the sliding BR door where there is an electric outlet also. When we travel, we just unplug and toss it on the bed. Does a great job of keeping the towels dry. Lots of choices and price points.