Even if you're not travelling through the south of Italy ( I haven't), you must do a day trip from Rome to see Pompeii. Read my stories on Pompeii and also Ophelie Quillier who has recently visited before you make your decision. I stayed a week in Cinque Terre. In Riomaggiore. I think if I returned I would stay in Manarola or Vernazza. I wouldn't stay in Monterossa. Day trips from Florence to all of the places you mentioned are perfect. We stayed in Calolziocorte in the Lake Como area. Get a rail pass! A church that I would visit in Rome is the Sant'Ignazio di Loyola. I won't tell you any more about it but I loved it! Somewhere I ahven't been but desperately want to see is the village of Valloria - the village with the painted doors! Can't get there by train though.