From another Cyn, and we had just 3 1/2 weeks, and were a couple, no kids. For what it’s worth, and this was in December 2012 (cooler than June/July, and maybe less crowded), but a wonderful trip:
Rome - 1 week. Museums and ancient sights galore! We rented an apartment in the Trastevere neighborhood, across the Tiber river from central Rome, but still close to sights
Flew to Sicily. Amazing food, warmer than Rome, wonderful people, fantastic sights. Rick Steves had done a Sicily TV program, but didn’t have a Sicily guidebook at the time, so the Lonely Planet guidebook was our main reference. We had about a week-and-half, and didn’t get to see everything we would’ve liked, and were pretty much on the move the whole time. A couple two-night stays, but mostly one-nighters, before driving onwards. We landed at the Palermo airport and drove our rental car west, to the Ancient Greek temple and amphitheater at Segesta, before heading to Erice for two nights. Then, going basically counter-clockwise, our visits included Agrigento, an agritourismo for Christmas, Caltigirone, the Piazza Armerina Roman villa, Modica (fabulous town and a chocolate destination), Siracusa, and Taormina.
We took a car ferry back to the mainland, and drove north through wonderful Calabria, including the town Caltagirone. We made our way to Sorrento, from where we made day trips to Naples, the ruins of Pompeii, the ruins of Herculaneum, and the Isle of Capri. New Year’s Eve and day were there.
Taking a train back to Rome on our next-to-last day, we visited the ancient Ostia Antica sight, before taking a taxi to our hotel at the Rome Fiumacino airport. We had an extremely early flight the next day, so opted for a room right at the airport.
Sicily, alone, could make an entire month’s holiday, but seeing Rome and other places south of it were rewarding. Other trips to Italy have been to places north and east of Rome, but we needed our almost 4 weeks to cover the ground we did in Rome and south.