Capri - relatively accessible by jet ferry from Naples
Florence - one of my favorite cities, with much to do and see - Uffizi Gallery, and the Academia are must sees.
Genoa - an industrial port city.
Naples - also an industrial port city (known for great pizza), and the gateway to the Amalfi Coast and Pompeii.
Rome - so much to see and do... the Vatican, the Colliseum - easy to get around walking and using trains.
Sorrento - a beautiful resort city. Once you get transportation to it, relatively easy to do on your own.
Taormina - just there - a quaint town built on the side of a mountain. A bit like an outdoor mall housed in historic buildings, but fun.
Venice - a wonderful city to just wander, and take water buses to different locales.