Merely urinating? One day, during the Abe Beam era, I saw a bum walking on the Bowery around 12 noon, in broad daylight, stop, drop trou, and defecate right in the middle of the sidewalk. When finished, he simply hiked his pants up and continued on his way.
In the Dinkins days, I saw a bum drop trou and take a dump on the Times Square shuttle during rush hour.