Past Culture Warriors have reported happy visits to the following places in Italy:

North of Rome

Florence

Venice

Cinque Terre

South of Rome, and near one another:

Sorrento (and Capri and the Amalfi Coast)

Pompeii

Ischia

They have recommended the following hostels:

In Florence: "Luna Rossa" on Via Nazionale, owned by Marco, with help on day trips and free internet.