I've never been down on the heel and instep of 'the boot' but I have been to Sicily. And a friend of mine has spent plenty of time down there over the decades. Both Bari and Brindisi are worth the visit, Bari has a large castle and also San Nicolo is buried in the cathedral. I have also heard some good things about Taranto and Lecce - there are also the famous Trulli dwelling in Alberobello.
The only place between Napoli and Sicily that I have visited by train is Reggio di Calabria, which has a nice coastline, away from the train depot.
When on the train to Sicily make sure your section of train is going where you plan to. Some of them split at Messina and part heads to Palermo, the rest heads to Catania/Siracusa.
Also be prepared for the occasional unexplained stop on the southern trains. I was once stuck on the track in Taorimina for hours while 5 train workers held picket signs in front of the train!