Sicily is a safe environment, safer than you'd believe from the hype. Although the Mafia still appears to be in control it will not affect the tourist . Some towns including  holiday resorts like Taormina have some degree of petty crime, so be vigilant but not alarmed it is no worse than anywhere else with high unemployment  and low police presence. For some reason in all of Italy there seems to be little done on crime prevention.   The police only seem to be visible when something happens and / or to stop drivers. Often they stand by the roadside with machine guns  which can be quite disconcerting !  Also some drivers in Sicily are not very polite or law abiding on the roads.

Sicilians are proud of their homeland and culture, and resist any change so don't expect  to be treated differently . When travelling you should take sensible precautions, especially in large cities like Catania, Palermo and Messina, You might not be able to blend in with the locals or want to, so all you can do is be streetwise and if unlucky just hope that one day they will tackle crime in a more proactive way. which is the only answer -.after all you are on holiday and if you should feel that a place is not going to be all that safe just don't go there.