We wash towels & washcloths once a week, after all how dirty are you when you get out of the shower - it's just clean water you're removing. We purchased a tension shower curtain rod (you can buy the plastic cover if it's a metal rod) and put it in the shower/tub area against the wall opposite the functional shower rod. This way wet washcloths can be hung up and used again without getting stinky and sour.
If each family member is assigned a different color - it works real well. You can also put a plastic hook with a clothespin built in and hang up other items too. More useful space - less mess!