As an Italian, from another region who has travelled extensively across Italy, I would highly recommend Sicily as a whole and in particular the East coast: Flying into Catania and potentially stay there with a rental car, I would recommend day trips to Taormina, Mount Etna, Siracusa and Ragusa. In Particular, Ortigia Island (the historic centre of Siracusa) it is worth a trip by itself.. Full of baroque architectures, but then with Greek/Roman archeology everywhere (the cathedral was built within a Roman Temple, and incorporate the original columns within the walls). Food is lovely there as almost everywhere and during the summer season, I would also recommend a bit of beach going by the Arenella Beach. Overall, there is so much cultural history to take in, at least on par with places like Naples/Pompei, Rome, Florence, and much more then other cities in the north of Italy.
but the island has so much to offer with history and derived culture from Greek, Roman, Arabs and Spanish influences