This is a perfect combo of my two favorite ideas for that space under the stairs leading to the basement. A reading nook AND book storage and shelves . assuming that there is enough space for this there.
Four wall-mounted drying racks in a mudroom create an instant indoor drying room; recreate the look with four wall-mounted racks from Ikea. For something similar, consider Ikea's wall-mounted Grundtal Drying Rack;
This classic pulley design is functional, rustic, and lifts your drying laundry out of sight until ready to be put away. Great for small laundry rooms. I would coat the wood so it can't mildew, which is what wood tends to do from damp laundry.
Line Indoor Clothesline Add 60 feet of drying space, then retract when done! Five cotton lines extend for over 60 feet of drying space in your bathroom, garage, mudroom or laundry room. When not in use, simply simply retract.
Tuck a retractable clothesline in to your laundry room cabinets to maximize your line drying space. Via Just About Home I already have the retractable clotheslines, but couldn't figure out where to put them.