Hotels are on to that. People at the beachside hotel I used to work at would use the room during the day to nap and shower, and then trh
Not only that, but how can you shower properly without being able to use a locker?
Sometimes just finding a bathroom I can use is difficult enough, and I’m talking about the city I actually do live in. The past few times I’ve been in DTLA taking pictures, I’ve noticed that none of the smaller establishments like coffeeshops have restrooms for customers, so I’ve just been using the ones at City Hall since I was going there anyway. I suppose one can also head to one of the hotels, assuming they still allow it, but it seems like one shouldn’t have to do that.
This is by far the best idea. I’ve couchsurfed a few times. I have friends who have done over 100 couchsurfs. If you have a decent profile just send out a message to 10 couchsurfers in the area that you’ll be visiting explaining what you’re looking for. I guarantee you’ll get at least a couple responses. For something as simple as a shower you’ll probably get even more.
… sneak in the gym, Tim…
Yeah, they’re ridiculously expensive, I think it’s because most truck drivers actually get them for free by saving up points on their ‘frequent shopper’ cards when they get fuel. If you’re in Ohio, showers are free on the turnpike, but then, it’s unlikely that you’re going to be hiking there. 
I visited Switzerland a couple of years ago, and there’s a chain of “McClean” pay restrooms in train stations there. They have toilet stalls and shower stalls. IIRC, they also sell toothbrushes, razors, etc. It cost me 2 Swiss francs to use the toilet* but if you wanted a shower it was considerably more expensive, like 10 or 15 francs. I’m not sure if that counts as “cheap” – at the current exchange rate that’s between $11-$17 US – but if anyone ever finds themselves in need of a shower in Switzerland then it can be done safely, cleanly, and legally without resorting to anything sleazy.
*This seemed rather shocking to me as an American, but there wasn’t a free restroom in the station and I really had to pee. For my money I did at least get a nice, clean restroom, like something in a fairly fancy restaurant.
If you are a pilot, the FBO at the local airport often has showers. Some places it’d be easy to use for non-pilots, other places not so much.
I never even really thought about that until reading this. I went to a very big state university. I had a lot of classes (none of them were science) in a couple old “Laboratory” buildings. The only male restroom in one building was an old locker room on the first floor that had showers.
… run through a sprinkler, Winkler …
Go for a hike, Mike…
… grab someone’s hose, Rose …
Off-the-wall thought:
How about a self-serve car wash? Some are of the automated, drive onto a plate variety, so it would be a question of what triggers the various mechanisms. Would a human being be able to do this?
Or there’s the self-service wand type, where the wand alternately dispenses soapy and rinse water. Some of these also have vending machines with towels or chamois cloths.
Considerations would be:
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Privacy. You’d have to find one that was not in clear view from the street, and you’d probably want to do it late at night. And cold weather might not be ideal. On the other hand, a lot of the automatic ones have doors that close or strips of cloth at the end that block the view of the car inside. I would think you could position your clothes out of the line of fire.
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Temperature and force of the water used. Too hot for humans? I’m not sure. And could you position yourself so that you wouldn’t necessarily get the full force of the soapy water or rinse water, which might be too intense in the automatic variety? (Also, the drive onto a plate types have a drying option at the end with heat and very intense forced air. But again…too hot?)
Cheap is relative. I think the wand type washes around here are less than $5.00, the automatic ones a little more.
Just thinking out loud…feel free to shoot down.
… jump in a lake, Jake.
Make sure your soap is Ivory. It floats.
Bad news, Ivory soap no longer floats.
… an’ getcherself clean!
…use a washbasin, Jason…
…don’t need to stay smelly, Kelly…
… share a jail cell, Mel …