Your passport hold three information that can be useful to you, but as other peoples already wrote (both in answers and in comments), it all depends on where you were born.
That said, this is what you should have on your italian passport:
Page 2, the one with the photos, has Place of birth. This is, obviously, the place you are supposed to be born for the Italian government.
Page 3, there are your residences. They are the place where you are supposed to be living, but if you are living abroad and never lived in Italy it will be less than useful
Page 4 (and 5, actually), and this could be interesting for you: those are the pages reserved to the authority who has redacted your passport. This is the authority that was in charge of your data and your identity as an italian citizen at the moment of your passport printing; mine, for example, report "Questura di Varese", meaning "Police headquarters of the city of Varese". Keep in mind that this not means your ancestors are from there, anyway.
Generally speaking, finally, all citizens data are centralized and your residence points to the city who is currently "responsible" for you, but that has not necessarely anything to do with your parent's place of origin.