For non-New Yorkers, Rudolph Giuliani was Mayor of New York between 1993 and 2001. He is credited with solving the city's crime problem, starting hyper-gentrification, and remaining calm on TV and being responsive to questions during the big 2001 terrorist attacks.
He first ran for Mayor and lost narrowly in 1989. In 1993 he ran a second time, against the same opponent, David Dinkins, and won narrowly. Either election could have gone the either way. The odd thing is that reversing either election turns out to have the same middle term effect, which is that Giuliani is not Mayor during the 2001 terrorist attacks.
If Giuliani wins in 1989, he probably gets re-elected in 1993, as IOTL he was quite effective during his first term, and leaves in 1997 due to term limits. If he loses in both 1989 and 1993 his political career is effectively over and Dinkins gets a second term. Either way, a standard machine Democrat pol is elected Mayor in 1997.
What are the effects past 2001? Honestly, my impression is that the crime drop was mainly due to other factors, and hyper-gentrification is more tied to Bloomberg, though it had been long planned or desired by New York City's elite, and I don't see how the city governments response to the WTC attacks would have been that different under a different Mayor. But I also had the impression that Giuliani managed the city bureaucracy well. I could be mistaken in all of these opinions. But I think starting in 2001 either POD starts attracting some butterflies.