The most classic itinerary in my book would be something like Venice (3 nights) -> Milan (1 night) -> Cinque Terre (2 nights) -> Florence (3 nights) -> Rome (4 nights).
I would probably replace Milan with Bologna in this case though. Not sure how the trains are to Cinque Terre from there though.
South is good but in my opinion the route I outlined is the best for someone who has never been to Italy just because you see the most (in my book).
Naples and Amalfi Coast are great but eh, not a fan for a first timer.
Sicily is one of my favorites, but same deal applies.
Venice is an absolute must for anyone that likes art, history and architecture.
