This is the ideal way to explore Sicily. Modern highways circle and bisect the island, making all main cities easily reachable. The A20/E90 autostrada connects Messina and Palermo; Messina, Taormina, and Catania are linked by the A18; running through the interior, from Catania to west of Cefalù, is the A19; threading west from Palermo, the A29/E90 runs to Trapani and the airport, with a leg stretching down to Mazara del Vallo. In general, the south side of the island is less well served, though stretches of the SS115 west of Agrigento are relatively fast and traffic-free.
You'll likely hear stories about the dangers of driving in Sicily. In the big cities—especially Palermo, Catania, and Messina—streets can be a honking mess, with lane markings and stop signs taken as mere suggestions; you can avoid the chaos by driving through at off-peak times or on weekends. However, once outside the urban areas and resort towns, most of the highways and regional state roads are a driving enthusiast's dream—they're winding, sparsely populated, and reasonably well maintained, with striking new views around many bends. Obviously, don’t leave valuables in your car, and make sure baggage is stowed out of sight, if possible.