If you have your own local currency on you when you arrive in Italy, the best place to exchange your own local cash is at Poste Italiane. You will need to show them your passport before the exchange.
I recommend checking if your own local bank at your home where you have your accounts can acquire Euro for you, some banks have Euro on hand, others have to order them, that takes a few days. I always buy Euro here at home ready for a few days' costs in Italia.
If you need to exchange your own local currency while you are still home, your bank may do that for you, or if Not, they may recommend a local international exchange office that will exchange local cash.
And as noted above, you can use your own bank ATM card at bank ATMs in Italia to obtain Euro. Before you leave home be sure to notify your home bank of the dates and country where you will be using your ATM card.