I've lived in the New York area for most of my life. The problem with Giuliani is that he can only function in a "crisis mode" in a jurisdiction that is normally run by incompetent leaders. He would be a marginal leader at best in any other part of the country, and most Americans would find the guy utterly unbearable.
Television adores Rudy, and I swear that's why he's the only Republican who'd stand a chance against the Witch Queen in the next election. Of course, rather than "adore," they worship Hillary. It'd be a close run thing.