Flying into Rome is easy... Flying out of Rome not so much.
I would recommend Nutmeg's entry/exit plan. We flew into Pisa and out of Milan on our first trip and that was very easy and surprisingly cheaper.
I am partial to the Liguria and Piedmonte regions. Small towns like Lerici and Alba are just so real and have very little tourist.
Of course Florence and Rome are number one on many peoples agenda, but for me walking the cliffs of the Cinque Terre or sipping an amazing Barbaresco in the village that bears its name brought Italy alive for us.
If you plan to hit the bigger spots make sure Sienna and Lucca make the list. Will be very curious what you final trip plans will be.