Airports are in Palermo and Catania. Check which airport has your routes. Near Catania you might come back a boat covered in volcanic ash. For Palermo (the airport is quite a bit west of the city) I would look at Trapani, San Vito lo Capo and Castellamare del Golfo, all of which have marinas (mostly one-pontoon small ones, but they're fine). There's a train route along the coast. Termini Imerese has a marina too, although never visited there so can't say anything about it.
Or park it in Licata and hop on the EtnaBus: €9.20 for a 2.5 hour ride to Catania.
Depending where you want to fly to, Ryanair fly out of Comiso or Easyjet from Catania both are relatively easy to get to from Marina di Ragusa which is a secure marina with probably the biggest live aboard community in Sicily.