Kristof, like many others of late, mention Rudy Giuliani as a possible Cheney replacement though he is not, in fact, possible in light of his pro-choice and (especially) pro-gay views. But beyond this, I wonder how much we really even know about his views.
In order to be viable in New York City he needed to emphasize his social liberalism and, of course, we know all about his theory of police management. My recollection of growing up in Giuliani's New York, however, is this. During the 1993 campaign the sort of white liberal Manhattanite circles in which I traveled were deeply skeptical of him and his program. In office, though, his program seemed to be working out quite well. So he cruised to re-election with pretty strong support everywhere outside of the African-American community and then seemed to have a very promising political future. He turned out, though, to be an extremely limited single-issue candidate. From January 1997 to September 2001 most people continued to appreciate his "tough on crime" tactics and, indeed, this became such a consensus view that all the major Democratic contenders promised to continue his appoach, though without the part of the strategy where he would act like a jerk every time the cops wound up killing someone.
But -- and it was a big but -- his anti-crime strategies worked too well. There was nothing new to be done on this front. And since his opponents wouldn't take the bait and propose reversing them, there was no content left to this agenda. And he didn't have any real ideas on any other fronts. So he could have continued on being a popular, do nothing caretaker mayor. But he had a kind of frenetic personality so he wanted to do something. But he didn't have any real commitment to other policy areas so he did not, for example, become a leading proponent of conservative ideas on education reform. He didn't have an economic development strategy beyond the (not far from wrong) notion that as long as crime stayed low business would keep booming. But this was still somewhat self-limiting unless you could fix the schools, where he didn't have many ideas. And his 2000 Senate campaign was looking like a flame-out even before the cancer incident. Senators don't change local policing policies and, again, he really didn't have any other issues.
On 9-11 he engaged in some effective charismatic leadership and regained his 1996-98 sort of popularity. Since then he's become one of these generic "don't you know there's a war on" kind of hawks, but he certainly doesn't have any foreign policy expertise. Indeed, his hawkishness seems to be 40% the Israel-pandering of any white NYC politician (listen to Chuck Schumer, for example) and 40% a desire to recapture the lost glories of September 2001. There's no real content to it. So that's really the tragedy here. He was a good mayor for his first term, and what was good about him became part of the New York consensus. But he didn't -- and, I think, never will -- manage to build on those accomplishments and play on a larger stage. He'll long be remembered in non-black New York circles as the man who saved the city, but also as a kind of disappointment. A could-have-been, not a was.