Mount mop and broom holders on the back of the closet door. (Try the Crawford Spring Grip; $4, acehardware.com.) They'll be out of the way and can air-dry. Even better, for ventilation, insert a screen panel on the lower half of the door.
As a tradesman, I like to venerate my tools with a respectable place in the home and out buildings. Tools are our friends. They feel the grip of our hands and know our thoughts better than we think they do. -Wf
Broom Storage: We have a small laundry room and needed some place to keep brooms, etc. We found a $50 drawer face on clearance for $10, added some hooks (single and double) to maximize usage and hung it behind the door. Loving this!