FYI: I've spent 10 days in Rome - it would be the #1, but this list is about places I've never been.
  1. Milan
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    Duomo. Quadrilatero della Moda. Corso Buenos Aires. Castello Sforzesco. Sforzo Park and Arch. San Siro Stadium. Day trip to Lake Como.
  2. Florence
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    Day trip to Pisa and Lucca. San Niccolo. Mercato Centrale.
  3. Cinque Terre
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    Get a train from Pisa. Riomaggiore, Manarola, Corniglia, Vernazza, Monterosso.
  4. Assisi
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    Umbria. San Francesco Basilica. Medieval streets. Climb Rocca Maggiore.
  5. Tuscany Villas
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    The Chianti region. Castellina. Panzano. Villa Flore. Brunello di Montalcino wine tour. Rent a car.
  6. Venice
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    Take the boat to the island of Murano. St Marks Square/Basilica.
  7. Almafi Coast
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    Capri. Monte Solaro. The Blue Grotto. Positano.
  8. Sicily
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    Palermo, Messina, Taormina, Catania, Agrigento.
  9. Verona
  10. Naples
  11. Siena
  12. Varenna