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Do not put a structured cap in a washing machine, and never put one in a dryer. Heat and agitation are what destroy the crown, and once the structure has gone soft there is no restoring it.
Cool water, a small amount of mild detergent, and a soft brush or cloth.
That is where most of the problem actually is. Cool water, mild detergent, soft brush, and let it dry completely before wearing.
Air-dry, away from direct heat. Stuff the crown with a towel or a ball of paper so it holds shape while it dries, and keep the brim flat rather than resting the cap on it.
Upright, not under other things. A structured crown will take a permanent dent if something sits on it long enough, and a flat brim will curve if you store it pressed against something.
Machine wash. Tumble dry. Dishwasher, this circulates as advice and it is bad advice for anything with structure or wool in it.
Every shop, address and detail is in the full guide, and the store map covers 21 states.