First Time in Italy - 2 weeks in September/Oct

With the time you have, I think Puglia (the southeast) is a better choice than Sicily. I assume you plan to have a rental car for at least part of the trip. Though you can manage without one (I did, twice), you can get around Puglia a lot more efficiently and see more with a car.

Sicily really needs at least two weeks by itself, and a bit longer is better.

You need a guidebook that covers Puglia comprehensively. There are lots of interesting places there (definitely including Lecce, and everyone wants to see the trulli around Alberobello), but we do not know what will especially call out to you.

We went from Rome to the Amalfi Coast (Praiano, Positano, day trip to Capri). I'm regretting not being more strategic in our planning as I want to see several other towns south of Amalfi (Minori, Furore, Salerno...I could go on) and want to go to Sicily. Pick a coast and stick w/ a plan. You can always go back to Italy on future vacations. There's so much to see and enjoy you won't go wrong no matter what you decide.

We also stayed in Airbnb places the whole way and it was great.

Terry I did a 2-week trip to Italy for my first time that was fly into Venice (2 nights there) > Florence (3 nights there) w/ a day spent on a tour of Chianti region > Cinque Terre (2 nights there) > Amalfi Coast (4 nights based in Positano) > Rome (3 days).

I stayed in the most amazing airbnbs in Cinque Terre and Positano, and found more local-style, family-owned hotels in the cities.

It was all by train and incredible!!! It wasn't too exhausting, but definitely a more active, get-a-sense-of-everything trip. Now I am going back in May for my honeymoon and only focusing on the North of Italy. I would say you could do what I outlined above or focus just on the South (as you outlined above) or just the North. All depends on your interests.

Feel free to message me.

Our 2016 tour was Venice 3 nights, train to Cinque Terre - Monterrosso, 4 nights, train to Siena, 4 nights, then private guide to take us from Siena visiting San Gimignano then on to Florence for 3 nights. We also like the air bnb style of lodging. Never rented a car.

Our 2019 tour starts in Venice again, then by high speed ferry across the Adriatic to Rovinj, Croatia, back to Trieste and fly into Naples, then train / taxi to Conca dei Marini near Amalfi. Back to Naples where we may rent a car for the drive to Tuscany / Montepulciano, and then finally Florence again where we felt like we didn't get enough time to explore last time. 3 weeks total this trip.

Not sure why you want to go South of Rome, there is a lot more to see in Italy North of Rome.
Still, you can come back and do Florence, Siena, Pisa, CT and Venice.

With two weeks, I would stay at least 6 days in Rome then head down to the Naples area. Find a good place to stay for the area and use it as a base. I did that years ago and stayed in Sorrento. You can take the ferry to Capri or take touts to the Amalfi Coast or Pompeii as well as visit the museum in Naples. You would need one day for Naples minimum, one for Pompeii, one for Capri, one for Sorrento and one or two for the Amalfi Coast. That doesn't leave you much time to go to Sicily or Bari.

Could you fly in or out of Naples, Bari, or Brindisi? If you don't have to backtrack, that would help considerably, but it's still doable.
I think you would be hard pressed to fit in Sicily--it would have to just be a smidgen of it, so I might hold off on that. There is no rule you have to spend several days in Rome--do what you want to do!
Just one sample itinerary if best flight option is Rome round-trip:
Arrive Rome, train to Naples 3
ferry to island (Ischia, Procida, or Capri) 2-3
ferry to Amalfi Coast (village of your choosing) 3
return to Naples (check Salerno transit options as well) bus to Matera (alternate, get a rental car in Salerno) 3
bus to Bari area (choose your town after research) 3
train to Rome for last nights--whatever is left
So, as you can see, you may need to omit something. The area south of Salerno is also nice if you decide to save Matera for a longer trip to Puglia later. There are lots of pretty hill towns, and you might get as far as Maratea in Basilicata. Too many variables at this point.

Hi Terry and welcome to the Forum.

Is there any way you could fly into Naples (NAP) and fly out of Rome.

Your itinerary would look something like this.

Arrive Naples, Curreri Viaggi bus-Sorrento 5 nights. This gives you ample time to Bus/ferry to the AC towns, visit Procida, my choice of islands, prettier and much less visited, visit Pompeii or Caserta, or Naples.

My daughter and I did this from her home in the Naples area last October.
Rent car in Sorrento and head to Matera 3 nights. Visit Ostuni, and Alberobello.
Then head to Polignano a Mare for a visit, and spend 2 nights in Bari. Head to Rome for your final 2 nights. Either by car or train.

This is a good crosssection for this area with limited drive times.

Here's a good blog which covers this area.

https://www.neverendingvoyage.com/8-towns-not-to-miss-in-puglia/#thebestareatostayinpuglia

You're going to have a wonderful trip.

Thanks everyone for the thoughtful suggestions. Looks like our best option to fly in Naples (1-2 days) first and then ferry to Sicily (6 or so days) from there and then do sort of a counterclockwise trip back around crossing back to mainland at Messina and then up to the Amalfi Coast to Rome (5-6 more days). If anyone has any additional suggestions based on this itinerary, they'd be most welcome.

Terry.