If I understand you forget everyone'w tip about their own favorite place. Go and discover your own! Staying out of Rome/Florenze/Venice lets you do it..

Head on south, stay on the coasts and and see the 98% of Itlay that no one else does, Go to Tropea ,where you can almost set your watch by what the the volcano erupt
see the rest of Italy. Just as many great things except everyone tells ou you have to go to Rom, florence or turscacy.