Centralized location in Provence, France

Do you mean Provence in southern France?
Sorrento is not on the Amalfi Coast though not too far away. You can visit the Amalfi Coast from Sorrento as a day trip.

Do you mean Provence? Not aware of a Providence in France. Provence covers a very big area, and even with a car, it's hard to recommend a central location that gives reasonable access to all places for day trips. What places are you interested in seeing? Mostly towards the west (Aix-en-Provence, Avignon) or the east (cote d'Azure)? If you haven't already done so, I'd recommend picking up a good guidebook to France to identify those places of most interest to you, then come back for more focused discussion.

As for the AC, telling us when in the fall will be of help. Late fall may mean less ferry service to some Amalfi towns. Also be aware that Sorrento, while a good central hub for exploring the area around it (Naples, Pompeii, Capri, and the AC) is not actually on the AC, but on the Bay of Naples.

Arles and Avignon are both good bases for Provence. I’ve stayed in Arles and prefer it over Avignon as a base.

7-8 days on the Amalfi Coast are a lot. One consideration you have to take into account is exactly when in the fall you will visit because ferry service along the coast comes to a halt. Spend 3 nights in Amalfi which is a transport center for buses and ferries. It’ll give you the opportunity to visit the fantastic towns in the area. On your way to the area, if coming from Rome, take the train to Salerno and bus or ferry to Amalfi. Then you could take the bus to Sorrento from which it’s easy to get to Capri, Pompeii, Herculaneum and Vesuvius. I’d also spend at least a long day in Naples as the Archaeological Museum is a “don’t miss” since it contains the artifacts excavated from the ruins of Pompeii. If you have an interest in Greek and Roman ruins, consider trying to take a day trip to Paestum.

Perhaps you are referring to the province de Provence?

As you have a car, I might recommend L'Isle-sur-la-Sorgue or St Rémy as bases. I generally stay in Avignon, mainly for the restaurants there and it is a bit more central to other locations in Provence than is Arles.

If it fits the budget, you might also consider Gordes as a base.

We were pleased with L'Isle-sur-la-Sorgue as a base a few years ago: central for day-trips in the region; plenty of restaurants, shops; scenic canals/waterwheels; the market days (Thursday & Sunday) are fun. We enjoyed a morning in St. Remy and would put it on the short list as a base were we to return.

Lots of attractive choices in the area. I think it would be hard to make a bad decision. You might want to use the Search feature above and peruse prior posts on Provence to help narrow your search.

Use ViaMichelin.com to check driving times from potential bases to the towns and villages you want to visit. I think having just one base is going to be rather limiting, even if you do not plan to see the Riviera on this trip.

If you opt for the longer end of the spectrum, 8 days, I suggest 2 bases, one further east, the other to the west. A lot of the driving in France is on winding hilly roads, which means short distances can take a lot longer than you think. Spending hours in a car day after day gets old fast.
In my opinion 8 days on the Amalfi Coast is too long. If you cut that to 5, you’ll have more time to do justice to Provence.

We used Avignon as a base our first trip. For our latest trip, 4 years ago, we based in San Rémy, easier for driving and parking a rental car.

We stayed next door to Sorrento, in Piano di Sorrento. The Sorrento area was great for exploring the Amalfi Coast and Naples/Pompeii region, both by rental car and train.

While touring Provence last year we used Gordes and St. Remy as our 2 bases. They were both delightful, had great market days and were easy to navigate as we drove from town to town. Make certain you drive and see Loumarin, Roussillon, Menerbes and Isle-de-la-Sorgue. These towns are delightful!
We used Sorrento as our base on our visit to the Amalfi Coast. Take the bus trip along the incredibly curvy road and see that gorgeous coastline, have lunch in Amalfi and ride the boat home to Sorrento. Try to take the day trip to Capri and see the island.....I did not years ago when there and I will always regret it!

We used St-Remy as our base this past May/June for 6 nights and it was great. I agree with another poster that you could cut time from the Amalfi Coast and add it to Provence. We spent four nights using Positano as our base for the Amalfi Coast (in addition to a stop in Pompeii on the way there). I think 5 or 6 nights would be plenty.

I agree with Cyn
I would stay in Sorrento and do day trips from there. I have used Positano for a home base in the past. More recently Sorrento as a home base. They are both beautiful but Sorrento has more to offer and greater access to the surrounding towns.
As France is... I can’t comment until after September when I return from my first visit.
Enjoy your vacation
Lorieann