After much thought and your help, this is what I've decided as my itinerary:
Day 1: Arrive Rome, train to Sorrento
Days 1-3: Sorrento, tour Amalfi coast, visit with La Famiglia in Lavello,
Day 4: Train to Rome
Days 4 -7: Rome
Day 8: Train to Florence
Days 8 - 10: Florence
Day 11: Train to Venice
Days 11 - 14: Venice
Day 15: Train to Rome
Day 16: Depart Rome
Any suggestions on how to spend my time in Amalfi, Rome, Florence & Venice would be greatly welcomed. As I said, I am a Chef, so food & wine is an important part of my tour, as is history....I'm not interested in seeing the first Starbucks in Italy, lol.