Walking around with your penis out and flopping around, in the manner of Dr. Manhattan in the Watchmen film adaptation. One truly going Manhattan style will affect an attitude of mild, bemused disinterest, and may perform dangerous activities that would generally require the genitals to be protected, such as operating dangerous, whirling scientific machinery.
“Ugh, did you see that homeless guy flash us just now?”
“Yeah. I was trying to ignore it, but that guy was totally going Manhattan style.”