Puglia

We did a trip to Puglia a few years ago; and decided that, in the interest of cutting down on lengthy drives, it was best to have two bases. We stayed at an agriturismo just outside Martina Franca, which, while nice, I don’t recommend. The town is steeply uphill from the surrounding farm land, so we had to drive in every night to get dinner. Parking was not easy.
Our other base was Lecce, which worked very well.
Matera isn’t in Pulgia, but I think we used it as a third base for seeing some of the nearby Pugliese sights.

Matera and Lecce are actually in two different regions of Italy—Basilicata and Apulia—
and 110 miles apart which is why most planning to include them in a visit split their stays into at least two locations. Lecce is a popular base for seeing Otranto, Gallipoli and Torre dell ‘Orso. With a car, you easily could stay in Torre dell ‘Orso which is in the Salento area with all its fantastic beaches. Lecce is a popular base also but is a larger city of 95K residents. Be aware in Lecce the Italian version of the siesta closes things up at 1pm and reopening time is 6 pm. That means things are only open 4 or 5 hours if daytripping to Lecce.
For a second base, you could stay in Polignano a Mare
to visit the towns of Locorotondo, Alberobello, Cisternino, Ostuni and Matera, which also is a larger city of about 60K residents.
Staying outside of the ancient city centers of the larger cities is probably a good idea time wise and traffic wise. That wouldn’t be as much of an issue in the smaller towns.

with 14 days in the area one option would be to spend about five nites in three places since the region is spread out. We stayed in Trani just outside the old town and didn't have trouble with car access, using it as a base to explore towns within 150km or so. We liked being in a small town and watching the locals during passeggiata as well as the choice of restaurants, having a drink on the harbor, etc. If I was planning your trip I'd consider a few small towns as bases since in a few minutes drive you're out of town.

One other area I'd suggest you consider visiting in addition to what you listed is the Gargano peninsula and the town of Vieste. Since you are interested in islands there are some off Vieste that you can visit (although we didn't do this)

Thank you John for your suggestions. I will certainly look into those options. We also like small towns and living like the locals. While I love the beach, this would not be a vacation to spend time at the beach. More interested in seeing the different towns/villages and maybe visiting a vineyard along the way.

We were in Puglia a year ago, and one of my favorite places was the agriturismo Trulli il Castagno not too far from Franca Martina. This was a good base for a number of nearby towns. The farm is simple but the host is outstanding. One night he did a Puglian dinner with wine pairings that was memorable.

I liked Lecce for a few days. Matera was amazing! Stayed in a wonderful cave hotel there - Corte San
Pietro. To really appreciate this city, do some reading and invest in a guide. (I wrote a trip report that might give some helpful info.)

Jacque, you don’t need to go to the Amalfi Coast to take a ferry to Ischia. The port, Is in Naples a half hour from the airport by taxi €18-22. Then an hour ferry ride to Porto.

This site will give you all the info you need on Ischia

https://www.ischiareview.com/how-to-get-to-ischia.html

I concure with all the other locations above except Vieste, while the area is beautiful, it’s more of a summer beach town. Taking a long train ride to get there. 4 hours 5 minutes is the fastest train.

We split our 2 weeks in Puglia between 3 places: 6 nights in Nardo' (on the Ionian Sea, on the Salento peninsula), 5 nights in the Valle d'Itria near Ceglie Messapica & 2 nights in *Rodi Garganico** (on the north shore of the Gargano peninsula).

Nardo' was enchanting & lovely. We stayed in the historic center, but it's such a small city that it was not difficult to park outside of the ZTL and walk in. It was our base for Lecce, Otranto & the amazing beaches of the Salento. A lot of Lecce stayed open through the midday pausa, to my pleasant surprise. Valle d'Itria was our base for all of the Trulli villages, Monopoli, Matera, Ostuni & Grottaglie (citta' della ceramica!). Rodi Garganico was more of a way station for our drive back to Rome - we visited Peschici while there but didn't make it to Vieste. If I had it to do over, I wouldn't have chosen Rodi, but it was an interesting area to visit.

ETA: trouble with formatting - I tried to make the first instance of Rodi Garganico bold but it's not working.

See:
https://community.ricksteves.com/travel-forum/italy/puglia-itinerary

We’ve always had a car in Puglia (and when staying in Matera), and except for Masseria Aprile and a rented trullo outside of Cisternino, we have stayed in the historic centers of all the towns and parked easily just outside the ztl. It really is worth a short walk (under 10 minutes for sure) to stay in the center. Or right at the edge of the center, like just inside the walls of Lecce.