Third trip planning help, please!

I don't have good advice on the itinerary since you are doing things we still haven't done, BUT whatever you decide, finish in Rome. so head for Sicily or Sorrento on day 1 (sorrento of course would be easy) and do what you plan to do and then spend your last few days in Rome where you need to fly from.

I sometimes go to my furthest destination and work my way back. You can get a flight that connects through a European city to Catania or Palermo (all on one ticket), then fly from Sicilia to Napoli (for Sorrento). Then Puglia, then end in Roma. But even with 3+ weeks, it seems like a lot of travel time. Keep in mind that travel is slower in the south. Roads are good if you have a car.

Assuming you want to spend a few days in Rome as well as in Sorrento, I suggest you consider spending the rest of your time in Sicily. There's plenty to do and see there. Puglia is also interesting, but public transportation there--as in Sicily--is not rapid. I spent more than two weeks in Sicily in2015, and I skipped all the classical sites in the SW (Agrigento, Segesta, Selinunte). I definitely could have used more time.

Have never been to Puglia or Sicily but thinking of seeing Puglia along with a return trip to the Amalfi Coast from Rome in the not too distant future.
A few places in the Puglia area that stood out to me:

Matera, Alberobello, Polignano a Mare

You probably already know of these 3 but if not you may want to research them.

Three plus weeks is a dream! We're going on our third trip in a couple months and only have 11 nights.

As Zoe says, best to go farthest away to begin with, so I'd book a flight upon arrival from Roma Fiumicino to Catania, Sicily. Don't make the connection too tight in case you're late arriving. Upon arrival in Catania, I can only advise you about Taormina and its environs, about 30 km to the north. Some say Taormina is too glitzy for Sicily, but all I experienced was beautiful, breathtaking scenery, awesome cuisine, nearby medieval villages like Savoca, Forza D'Agro and Castelmola, and of course Mt. Etna if you so desire. I loved it.

You can do that area in 3-4 days. If you want to do the rest of the island right, figure an additional week at least, and Zoe or others schooled in Sicily can advise you on the somewhat-wonky logistics at times. Personally, I'd love to have the time to do it! If not, you can take the train which is placed on a ferry to traverse the Straits of Messina back to the mainland, and then move on to Puglia upon arrival. Yes, the caves of Matera on the Basilicata/Puglia border supposedly are wonderful, but I'd check out Bari and Polignano a Mare on the Adriatic coast as well--they'd probably be a little less traveled in high season.

From there, head on back west across the breadth towards Sorrento. Remember, there are no Freccia (fast) trains in the east and south of Salerno in Italy so you're going to have to be OK with the quirkiness of the train scheduling. But with 3+ weeks, it shouldn't matter, and should be an experience!

Sorrento--where we're going in March--should be a wonderful base for daytrips and at a perfect time of year weather-wise. You may--just for the heck of it--want to stay a couple days in Salerno first to see a small city operate. The Old Town is wonderful, and the ruins of Paestum are 40 minutes to the south as a daytrip. But if it were me, after that I'd be staying a week in Sorrento proper, visiting Naples, Pompeii, Ercolano and Capri during the day, maybe even take the SITA bus over to your old favorites on the Amalfi Coast.

When finished there, you can take the Freccia from Naples to Orvieto. We will be visiting there as a daytrip in March but I hear that in high season (as September/October is) the best way is to stay overnight in Orvieto for the quietness after the daytrippers have left.

If you still have a week left, you could do far worse than to finish up in Rome. Find yourself an apartment through VRBO or AirBnB, and chill in a quiet neighborhood, frequenting the markets and espresso shops.

Enjoy your planning!

Are you planning to drive?
I would fly to Palermo from Rome, and then pick up a hire car.
After Sicily, catch a ferry from Messina and head thru Calabria & Puglia before finishing up in Sorrento.

We've been to Sicily for five weeks total, Puglia/Basilicata for three weeks total - all by public transportation. We've also stayed in Sorrento for a couple of nights. My advice would be two weeks in Sicily, one week in Puglia and skip Sorrento.

I enjoyed Sorrento, but I was there in winter when there were few tourists and I used it mostly as a base for Pompeii, Naplies and Herculaneum. Unless that's what you want, skip it.

I haven't been to Puglia, but I spent 2 weeks in Sicily, flew Alitalia into Palermo (transfer in Rome), after Palermo and Cefalu, I rented a car for the duration. It's a very big island with stunning sights - Greek temples, Norman churches, pristine beaches, and terrific food. I would say 10 days is the minimum and even with 2 weeks, you'll skip have to skip a lot.

You'll definitely want to fly at least one way to or from Sicily. You can start with Sorrento, then fly from Naples to Sicily (direct bus from Sorrento to the Naples airport), then drive around Sicily, then drive back up to the mainland. Or, you can start with a flight from Rome to Sicily.

If you are planning to fly to Sicily upon arrival in Rome, you may want to do what I did. I booked two tickets FCO to PMO - one three hours after my arrival, and one ten hours after my arrival. I knew I'd use one and throw away the other, and the total price of the two tickets was less than a last minute ticket on my travel day (a Monday). In the end I made my three hour "connection" with time to spare, but I could just as easily have missed it.

While Palermo is a bigger city, Catania has a bigger airport, with more flights. To see the island, it's usually best to fly into one and out of the other; if you're driving one way to or from the mainland, fly in or out of Palermo (since you will start or end in Messina).

From Rome, both Palermo and Catania airports have lots of options; from other cities on the mainland, there will usually be 1-2 flights a day to the Sicilian airports. Check Skyscanner for all options: http://www.skyscanner.com/

Note that Alitalia has a more generous carry on allowance than budget carriers and allows one free checked bag, so in the end it can be cheaper or the same price as a "budget" carrier. If you want to book a domestic Alitalia ticket, do it on their "International" website: https://www.alitalia.com/en_en/. This has the same prices as their Italian website, but has an English language option. Their US website often has much higher prices - for the exact same flights!

My Sicily trip report is now over two years old, but should still give you some ideas. Spoiler alert: I loved Taormina, and even the tourists can't ruin its magic atmosphere. And for cultural experience and markets, Palermo is wonderful. https://community.ricksteves.com/travel-forum/trip-reports/sicily-palermo-caltanisetta-siracusa-taormina

Thanks for all the great ideas. After too much thought, I am deciding to leave Sicily and Sorrento out of the mix! Logistically, it got to be a little crazy (I want to go here, I want to go there, can't be in Sicily without seeing this or that!) and I had to step back and really think about what we want out of this trip. Ever since our last trip to Italy, we have wanted to go back and experience the culture and relax in small-town ambiance, go to some cathedrals, castles, outdoor markets, whatever looks of interest. I am now considering going to Ponza first after arriving in Rome (3-4 days). Being close to Rome, we can recoup from the trip and do some boat excursions around the island and chill out. Then train to the Adriatic Coast and stay in Termoli or Polignano A Mare, perhaps renting a car and exploring at our leisure, or just using the train system. After twelve or so days in Puglia area, train back to Orvieto or Lucca (and/or ?) and do whatever day trips we feel like doing at the time. Finally returning to Rome for perhaps one night before departure. Any comments?

I think that sounds fabulous. Ponza was totally off my radar but from some YouTubes I saw seems like a great, different way to unwind from jet lag and then some. And you can--to a certain extent--make the rest of it semi-spontaneous over on the Adriatic coast, although I would still research and reserve lodging over that way just to be sure. And being quasi-at the whim of the Italian 'interesting' rail system--not the fast Freccia lines--is always an adventure.

The fun of having this amount of time to travel, and it also not being your first rodeo to Italy, means you can--and it sounds cliche'd--'see how the Italians live'. Be one of just a few tourists in an area, staying away from Rome, Florence, Venice, making camp in a town and having that village's vibe envelop you.

Enjoy your planning!

I could not agree more with Jay. Such a different experience being in a smaller town. By your second visit, the restaurant staff will remember you!