Napoli is a shithole. It's out of the way and ugly.
If it were me, I'd probably spend most of my time in and around Abruzzo, but for you and others that probably want the canned and condensed version of Italy I'd say spend three or four days in Rome to see all the touristy stuff there before you cross it off your list and put a notch on your belt. See the various duomi, order a beer at McDonald's, eat at trattorias, see the Coliseum, Vatican, try to find your way around using the embedded stone street signs (vaffancuolo! that guy in a suit on the moped cut me off and I turned down Via Innocent III instead of Via Innocent II), etc.
Firenze is nice. Spend three days or so there for the shopping and the more refined beauty of its tourist traps. Gelato by the Piazza della Signoria, get robbed by gypsies, give a Euro to the Albanian with one leg, etc.
Stop by Pisa after Florence for another notch.
If you want Italia and not Italy, I'd say rent an old Fiat and hike it up Gran Sasso. Then maybe head to Pescara to watch women strip down and tan on their lunch breaks, get gelato by the beach, have a full dinner at a local restaurant (calamari zuppe, whatever seafood was caught that day, poached pears, etc.), then pack up and get ready for the trip to Sulmona for the confectionaries the next day. From there you can take a train to pretty much anywhere you want.