I'd have to say, Antonino (Anthony) Accardo, a/k/a "the Big Tuna"/"Joe Batters"! He never spent a night in jail, never did any time in the pen, NOTHING. Managed to run the Outfit for close to 50 years, while everyone, including the "G", didn't have a clue! Others stood in as boss while "JB" was laying low
staying under the radar. His biggest/boldest move, that the public could and would scrutinize, was his purchase of a mansion in a nearby Chicago Suburb, he ended up going through 3 before his death by natural causes of congenital heart failure at a hospital not far from where he grew up as a child.
I understand that Chicago is no New York and things regarding organized crime are plenty different.