Rome's historic center (near Pantheon, Campo de' Fiori) is ideal but pricey; Trastevere offers more local character. Florence's Oltrarno district across the Arno is charming and slightly cheaper than the center. Venice is expensive everywhere — even modest hotels cost significantly more than the mainland.
Agriturismos (farm stays) throughout Tuscany and Umbria are excellent mid-range options combining accommodation with home-cooked meals. The Amalfi Coast's cliffside hotels are among Italy's most spectacular, if your budget allows.