Consider drop down hooks for hanging clothes right out of the dryer. They can handle several hangers and can be put up against the wall when not in use.

Or run a pole over both the sink and washer and dryer from wall to wall. If you have drip drying to do, then it can be hung over the sink and the entire rod can also be used for hanging shirts, etc. right out of the dryer.

I am in the middle of trying to find cabinets that will fit above my washer and dryer so I have storage for detergent, pre-wash, bleach, fabric softener, and other cleaning supplies. Like you, I don't have much room above because of door, access to coat closet, vent etc. What about a corner cabinet?

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I would remove that clock, why do you need to know what time is it in the laundry room? What I do need in is a laundry room is .... 1) some space to set a laundry basket, fold clothes, etc ... and that little rack you have there doesn't look like you could really use it for anything functional and it looks like it blocks the dryer door from being able to open very far. So I would remove that. 2) The other thing I have to have in a laundry room is a bar to hang my wet clothes that don't go in a dryer. 3) And I need some storage space/cabinets. 4) It's nice to have an area for a clothes steamer and an ironing area. So without seeing the entire space I can't really say how I'd make that space not only prettier but more functional.