Not just urinating in general though, but actually doing it away from a lavatorial environment.
Now in Tokyo there are many things that you are expected not to do in public, as for whatever reasons they are deemed socially unacceptable. So blowing your nose is out. As is eating on the train. Likewise kissing in the open is simply not the done thing.
Urinating wherever you please however is just fine. Of course I’m not saying that people are pissing here there and everywhere, but at the same time it’s not unusual to see a barely concealed gentleman emptying the contents of his bladder for all to see.
Still, as long as he isn’t blowing his nose or eating at the same time, I guess it’s ok…