It is absolutely safe in Catania during the day if you observe the standard precautions. People here are very open and friendly, many know English, the streets are clean and beautiful. However, in crowded areas, pickpockets and thieves on scooters are prevalent.
With the onset of darkness is not recommended to walk in unfamiliar areas, look into the dark deserted alleys. All central streets of the city are heavily patrolled by police and military.
Try to avoid evening strolls in market areas Fiera, Corso Sicilia, Pescheria.