pinball petes arcade in ann arbor locks its bathroom and have to ask for a key.
the starbucks upstairs is open and does not require a key.

the starbucks at warren + woodward requires a key.

this is a major issue in all big cities.

searching for public toilet new york brings up a slew of articles, from 1991, 2000, 2005, 2012 etc. all the same problem. 'not enough toilets'.
http://www.nytimes.com/1991/05/21/ny...any-rules.html

its not just detroit. theres a serious lack of restrooms in all of SE michigan.
even the suburbs. i've taken to stopping at various hospitals to find open restrooms.
most of the hospitals in detroit have locked restrooms... at least hutzle on st antoine and henry ford on grand blvd.
kresge might have open ones near the pharmacy.

libraries, fast food, grocery stores, gas stations. good luck.