Calabria or Puglia or somewhere else

Although I have not been to Calabria, it is on my list as a nature lover, so I have poked around at planning. I believe coastal Calabria would be easiest without a car. Moving inland may be more complicated. See this as an indicator of that: https://www.wanderingitaly.com/maps/calabria-rail-map.html
The coast and avoiding the beaten path can be difficult, but I would not worry about June like I would August.
First, I would look at flights to Lamezia Terme and Reggio Calabria. Flying into Naples and taking the train south works (as would flying into Catania and heading north), but it does eat into your time, so I would first compare all flight options to see what works best.
If your son wants to meet you in Naples, then you could set off from there for Puglia and travel around fairly easily. (You can also check flights into Bari and Brindisi).
You will for sure have to pick one or the other--nine days will go fast!

Fly into Lamezia. You can visit the Albanian villages in and around the Pollino Park. Small hill towns like Belmonte Calabro (not during afternoon "pausa" as I learned). (That with car only, so maybe its out for you..)

You could visit small coastal towns like Amantea (close to Belmonte) and Diamante, famous for its red peppers.
Always keep in mind the "pausa," when everything except restaurants shuts down in mid-afternoon.

Visit Reggio if you want to see the bronzes.
Tropea or Scilla for beach (you can get a ferry to Stromboli from Tropea, I believe); book hotels in advance as the beaches get tons of tourists
Aspromonte Mountains to get up into the hills....

There's a great book about Calabria called STOLEN FIGS by Mark Rotella, an American of Calabrese origin.

Puglia is another story entirely.

Actor Stanley Tucci features Calabria in an episode of his Stanley Tucci: Searching for Italy series. His ancestral province and is joined by his dad and mum.

Better than any written guidebook. He eats at a rural restaurant La Collinetta, which is a well disguised gem, and hard for tourists to find. Even with a car. In particular at the end of the show is featured the Calabrian relatives preparing food for a family feast and the feast that follows. Should be doing the rounds on a food channel on cable somewhere. A wonderful occasion should one be blessed to experience anywhere in Italy.

The unique experience of eating food and drinking wine, away from the major tourist centres of Calabria is that it will be/is different from anything that you will have experience in the north or elsewhere. Will it be good? Indubitably! Will it measure up to your expectations and palate as good. No idea. Hope you like swordfish fillets/cutlets.

Cannot give an itinerary as my family insist on driving. Crazy Australians with a little Italian DNA somewhere.

Tropea is charming city. We have stayed there twice and enjoyed exploring and experiencing.