The dream setup for a public wedgie for me is that someone would see me, and either make fun of me or just take over and start wedging me. What you don't want is to be a public creep and weirding people out or have them report you or something.
To that point - I really like doing wedgies in a public bathroom, but in the open area. You have a lot of control in regards to if / when someone might see you. Like are you giving yourself a wedgie already and someone walks into the bathroom, or do you wait to give yourself a wedgie till you know someone is going to turn around and see you?
I think the most important thing is to just be cognizant of the type of person you'd likely see in a certain public place. A locker room in gym is going to have a much more predictable crowd than a Walmart aisle!
Also don't do it somewhere that a coworker or someone you know is going to stumble on you