Of course you know all the travelling rules very well. Sicily is less dangerous than Rome, Paris or London, though there are places where you should be careful. Take the same measures as everywhere.
In Taormina be attentive with ATMs in crowdy places. Look out if there are signs of criminal activity - false fronts, loose or bulky card slot or loitering strangers trying to steal your PIN. Do not use non-bank cash machines.
In Catania and Palermo do not leave the car unattended and with luggage or anything attractive inside, even in the boot. When you travel by car, do not keep the bag on the seat as smash-and-grab criminals may break the glass at the traffic-lights.
Walking the streets keep your bag or camera on the side away from the traffic, there can be thieves on motorbikes. And you'd better not wear expensive clothes and jewellery going to big cities. But you can wear them in Taormina as the whole historical center is guarded by video-cams.