Italy was safe for periods of the Republic, depending on where you lived. Rome fought wars to unify Italy from the conquest of Veii c. 396 BC down to the taking of Tarentum in 272 BC. Once Rome controlled most of the Italy after the Samnite Wars ended (290 BC) then you would have been safe from any organised aggression as long as you weren't fighting Rome. Thanks to Hannibal, Italy became extremely dangerous again in 218 BC until he got kicked back overseas in 203 BC. Rome then had to engaged in punitive behaviour to punish Italian cities and states that had betrayed them during the Hannibalic War. Considering the Gauls got knocked back once and for all Telamon c. 225 BC, once all that settled down Italy would have been pretty safe again until the Germans came rolling through c. 105 BC and destroyed two consular armies at Arausio. Marius sorted this out a few years later, but Italy was no longer particularly safe as the civil wars begun in 91 BC with the Italian allies rising up, and civil war continued intermittently in Italy until around the 40s BC when I think most of the fighting moved overseas.

Once Augustus had set up a nice and stable monarchy, Italy was very safe indeed, with scares from the Dacian (AD 6) and German uprisings (AD 9). But Italy was not the target of foreign violence again until the Marcomanni attacked Italy c. AD 168. However, civil wars had occurred after the death of Nero (Year of Four Emperors, AD 69 and later after Commodus (Year of Five Emperors, AD 193, fighting until AD 196). Around this period and later Italy was more commonly exposed to civil conflict and rarely foreign aggression, and my knowledge starts to run dry at this point.

tl;dr: It was probably safest during the pax Augusta c. 27 BC-AD 180, with the exceptions of the Year of Four Emperors (AD 69) and part of the Marcomannic Wars (AD 166-180).