If someone is not a conservative, that doesn’t make them a liberal, as appealing as a black and white world is.
Guiliani himself has said he ran a ‘fusion’ candidacy for mayor of NYC, picking up elements of the Democratic, Republican, and Independent Parties.
The most accurate term to describe Guiliani is a ‘moderate’ or ‘independent’.
I would say he has absolutely no core beliefs. He's not conservative, liberal, or moderate - - he's whatever he has to be.