I hope you will get a chance to see the incredible 3000 year old olive trees all around the Ostuni region before heading to Lecce, Imagine these trees were planted 1000 years before the birth of Christ. They are huge, twisted hulks like nothing you will see anywhere else in Italy.
Heading south from Lecce...
Otranto
Otranto is a nice stop, the Cathedral of Santa Maria Annunziata has 800 skulls behind the altar (When 20,000 Ottomans invaded Otranto in 1480, the locals refused to convert to Islam and were beheaded) and an amazing mosaic floor called the tree of life from the 12th century, the floor is worth the trip in my opinion, there is also a small fortification.
Amastuola Wine Resort
In this area you can also book a tasting at this winery if it is open. We had a great afternoon here the people running the place were great and wouldn't let us leave.
Gallipoli
Not the WWI Gallipoli, but a town on an island you can reach by car over the bridge. The Hypogeum Oil Press is worth seeing if you haven't already seen an underground olive oil press, they fortified these and put them underground in this region because of the value of olive oil back in the 1500s. When you see it remember the donkeys lived down here with the workers to run the pressing stone. There is a small senic fortification the Castello di Gallipoli to see. The town is small and you can walk the perimeter around it or transect it through the narrow alleys for a great Italian village local experience of what you will find.
Then you head into the Basilicata Region, here you will make up time driving as the sites are fewer and you will be on the eastern coast heading south...
Greek Ruins of Metaponto
Worth an hour or two if you like these things, the Temple of Hera is the most impressive
Heading in from the shore is the ghost town of Craco. Not sure how aware you are but there are dozens and dozens of Italian ghost towns in southern Italy, typically due to earthquakes and bad building locations. Craco is one of them, the views from the village out over the valleys surround it are crazy beautiful. You get into the town via a tour you can take when you show up.
If you want to do some hiking Pollino National Park in Basilicata is the place.
Sooner or later you will have to decide do you want to stay on the eastern shore all the way down to Reggio Calabria or sneak across to the west side and continue south. The east side is going to be less populated and less traveled, Ciro is a wine town the birth of the oldest wine in Calbira. You can go to the hilltop town of Gerace. Another hiking place is Mount Tre Pizzi from Ciminà, easy hike to some amazing views. This would also get you into the village of Cimina and access to the cheese called Caciocavallo di Ciminà, delicious and I would guess you've never seen a cheese like this one before. There is also the tiny village of Stilo off the beaten path. This tiny Italian village has a small Cattolica with fresco remnants from the 16th century, the exciting thing about the church is the walk to get to it. There is also a castle at the top of the mountain above the village you can just about drive to and then a short walk to explore it which you will have absolutely all to yourself.
Then you reach Reggio Calabria and hopefully you have on your schedule to see the Museo Nazionale della Magna Grecia and the two full size human statues they pulled out of the sea (Riace Warriors) on display there in the wild environmentally controlled room you have to enter to see them a few people at a time.
On the way back from Sicily take the west coast back, this is the more populated, large towns, with resorts and beach goers, with well-known towns like Scilla (the Venice of the south) and Tropea a wellknown beach town. Heading north along the coast are sites like the Grotta del Romito Caves and the huge statue Statue of Christ the Redeemer of Maratea.