Like you said, find a restaurant, or a Dunking Donuts and buy something...or just sneak in. Look at the menu up as you're thinking and then run to the bathroom. At the places I usually is it I don't feel guilty, if I ate there yesterday I paid for today's bathroom use :)

Public bathrooms are a lot of trouble with cleaning, crime etc and usually are closed at nighttime in parks too. Tech can mitigate some of those concerns but still...