Does this make sense - Itinerary

Also plan to rent car after staying in Naples to drive to Puglia. Should I keep car in Sicily or leave car in Puglia, train it to Sicily and rent car there? Just concerned about drive there, don't want to stress.

Where to stay in Puglia sort of depends on what you're most interested in seeing. For me, I'd stay in Lecce. The town is beautiful and the beach is close by, about 20 miles if I recall correctly. I also liked Otranto. Lots of people like Polignare al Mare, but the beach was small and crowded when we were there. For the beach and nightlife, Monopoli is good, but it's a bit far from everything else to use as a base. It really depends what your priorities are. The distances are lot great, but driving takes longer than you'd think.

We've been in a holding pattern on our trip to Sicily for over a year, but just from my planning, I'd say leave the car in Puglia, fly (from Bari or Brindisi ) to Palermo or Catania, and pick up a car there. The train from Puglia to Sicily is not great. Taking a train, bus or car and a ferry will take at least twice as much time as it would to fly. And, keep in mind that some rental companies to not permit you to take their car on a ferry. As for which towns in Sicily, have you looked at the RS or Lonely Planet books? Both give suggested itineraries, but again, it really depends on your preferences -- cities/museums/markets, Roman ruins, beach, staying in a agriturismo for some downtime in the countryside, or seeing Mt. Etna/vineyards. With only 10 days, you're probably going to have to narrow it down. That will also help you decide whether to fly in Catania or Palermo.

I can't address your question about whether you should drive from Puglia to Sicily because I don't drive in Europe. You can check estimated driving times on ViaMichelin.com and compare that to the rail schedule. Definitely check with the rental-car company to see whether you will be permitted to take the car on the ferry across the Straits of Messina. Also check on drop on the drop charge. Edited to add: Wanderlust's suggestion to consider flying is a good one.

I urge you not to drive in Palermo. The traffic there is crazy even when you're wandering around on foot. I can't imagine driving in that. So I'd recommend ending your trip in Palermo and dropping the car there upon arrival (perhaps having seen Monreale on the way into town--see below). Of if you fly into Palermo, you should wait to pick up the car until you've done the Palermo sights and probably also Cefalu.

Ten days isn't really enough time to cover all of Sicily, even with a car. As someone with only the most minimal interest in classical ruins, I'd definitely make Siracusa (Ortygia neighborhood) and Palermo two of my stops. After that, it's more difficult for me to prioritize. You could easily just divide your time between those two bases. There are lovely Baroque towns inland from Siracusa that can be treated as day-trips, though Ragusa seemed worth an overnight. Palermo is a major city with a lot of local sights (including two wonderful food markets), but there's also an easy day-trip to Cefalu by rail. The magnificent basilica outside town in Monreale can be reached by public bus or tour bus if it's not convenient to see it while you have a car.

Over-touristed towns full of international boutiques set my teeth on edge, so Taormina didn't much appeal to me and I wouldn't want to spend the night there. However, if is a very pretty town in a lovely hillside location, and it is popular. Mt Etna is in the neighborhood, and Catania (while ranked behind some of the other cities by most visitors) has an attractive historic center and a WWII museum (which I unfortunately haven't seen).

Alternatively, you might consider spending a night or two in the interior of the island, perhaps in Piazza Armerina, Enna or Caltagirone. The Villa Romana del Casale outside Piazza Armerina has wonderful mosaics, and inland Sicily is quite different from the coast. It would be shame just to hug the coast if you have a car.

I also liked Trapani and its medieval neighbor, Erice.

Others will be able to suggest the best way to see one or more of the major Greek sites (Agrigento, Segesta, Selinunte) by car. If you have only slight interest in such things, you may be satisfied with the Greek theatre in Taormina and/or the archaeological park (with Greek theatre) in Siracusa.

Would you consider skipping Rome altogether on this trip (on the theory that Rome will always be there and is easy to get back to) and flying straight from the Rome airport to either Naples or Palermo, or to Brindisi or Bari in Puglia? You can also fly one way or the other between Lamezia and Palermo --- we have driven and taken the ferry from one to the other and it was not fun and took forever.

Absolutely rent a car while in Puglia and also after visiting Palermo to tour around Sicily (my husband actually enjoyed driving in Palermo and Naples and Rome but he is an unusual person). The roads are fine (considerably better than roads in Minnesota) and the only real thing to remember is that you have to drive to a parking area outside of every town center, then walk into the historic district. I am assuming that you would read up on driving in Italy, both the laws and the customs.

We've never done it, but driving from almost anywhere in Puglia to Lamezia would not take long and looks interesting.

In Puglia, you could spend half your nights in a town (the historic centers of Lecce or Ostuni are our favorites) and half in the countryside either staying at a masseria (a B&B farmstay) or renting a trullo. It sounds as though you don't mind short stays as much as we do, so you could even stay in three places in Puglia. I should say here that we have never been to Puglia in the summer, only in spring, fall, and winter, so I imagine it is a very different place with all the beaches and beach towns open.

For recommendations for specific places to visit and places to stay, I would need more information about what you like to do. We love all the Romanesque churches in Puglia, for instance, but they would not be everybody's cup of tea. Especially after the first two or three...

concerned about drive there, don't want to stress.

If you are concerned at the idea of driving in rural Sicily you shouldn't drive twice through the Apennines. Especially because you are not interested in visiting Matera on the way to Puglia.

The train travel from Bari to Palermo takes 15 hours and 2 changes. Just take a train from Lecce to Bari Airport and fly.

There are night ferries from both Naples and Salerno to Sicily. You could visit the same areas the other way around and leave Rome for the last days of your trip.
Something like: fly to Naples > private transfer to Positano > Positano > ferry/bus/taxi to Salerno > Salerno > night ferry to Catania > Sicily > fly to Bari > Puglia > train to Rome > Rome > Home

ps Google "ZTL fines"

Check out Easy Jet for flights from Brindisi or Bari to Palermo. Very reasonable. It will take to long to drive from Puglia to Sicily.

And the train trip from Sicily to Puglia was scheduled to take so long in 2015 that I opted for a bus instead.

Thank you for all your good points I will defininately consider changing my itinerary. I enjoy reading everyone's advice on this forum.