Alright, we're gonna lose some of you with the title alone here, and that's fine.
But for the rest of you...
The Cleveland subreddit
has been discussing this very question over the past 24 hours, and it's a worthy one. If you live, work or play downtown, you've had this conversation with friends, we're sure. Because when you're staring at a single busted stall in the Warehouse District late at night or enjoying a dizzy Browns Sunday at a packed bar with the remnants, litter and scattered garbage left over by what must be animals and not humans who used the stall before you, you wonder if there is a safe haven when nature calls.
You'll have to dig through the thread for what emerged as the most unique suggestion so far, but here's a short roundup of the most useful tips.
Casino. Open 24/7. Bathrooms are clean
On the topic of the Tower City food courts:
Oh god man. Never go there.
An alternative at Tower City:
There are other restrooms back where the movie theater has an exit, walk past FYE towards the popcorn shop, its down a hallway by the lottery store(141) http://www.towercitycenter.com/assets/images/directory/directorymap.pdf
I dont think this area gets much traffic. Its my go to restaurant if I am coming in from Akron early in the morning and really have to go
Guest bathrooms on the second floor of the Ritz Carlton, above the bar, where conference rooms are right up the escalator at the end of the public square lobby hallway. Each stall is its own tiny private room.
Nice hotels usually have awesome lobby bathrooms. Usually when I'm in strange cities I hunt out nice hotels nearby to drop some heat, I'd imagine the same holds true here.