We just did your itinery minus Nice with 11 days in Italy starting in Rome and ending in Venice. It was amazing! Here's what we did.
1 night on plane, 3 nights Rome, 4 nights Florence with day trips to Pisa, Cinque Terre and Sienna, 2 nights Venice
Day 1 Flew to Rome from U.S. 9 or 10 hr flight overnight
Day 2 Arrived Rome airport 6:40am, checked in apartment at 11am. Piazza Navona, got groceries, did Pantheon day and at night, Trevi Fountain. Recovered from jet lag/time change.
Day 3 Rome – Capitol Hill, did Through Eternity Tour of Colosseum,
Forum, and Palatine Hill from 3-6:30pm , Spanish Steps.
Day 4 Rome - Vatican Museums and Sistine Chapel, St. Peter’s Basilica Tkts for 11:30am,
bought online prior. Evening: Campo di’Fiori, Piazza del Campidoglio.
Day 5 Checkout 11am, left luggage, walked to Trastevere and back. Got luggage and taxied to Roma Termini; Trenitalia train to Florence 2:50-4:22pm, Frecciargento 943. Bought these tickets online from home as soon as they went on sale and they were only about $20 each. Same for the ones to Venice. Arrived Florence. Taxi to apt and checked in. Piazza Della Signoria, Palazzo Vecchio, shopped.
Day 6 Florence – Piazza della Repubblica (arch/carousel), climbed Campanile Bell tower, toured and climbed Duomo, museum, San Lorenzo Market, dinner at Mercato Centrale (food court). Night - Ponte Vecchio bridge, Pitti Palace
Day 7 Day trip to Pisa and Cinque Terre with Tuscany on a Budget Tours, This was amazing!!!!
7am-8:30pm, Pisa - Climbed The Leaning Tower, cemetary, church and baptistry, then 3 CT towns: Riomaggiore, Vernazza, Manarola. Trains and a bus at Pisa
Day 8 Day trip to Siena – Took 1:10-2:25pm SITA bus from station by Santa Maria Novella.
Day 9 Firenze S.M. Novella station train to Venice; Frecciargento, 10:15am-12:20pm. Rode Vaporetto boat to Zacarria stop, arrived Residenza de l’Osmarin 1:45pm. Saint Mark’s Square & Basilica, wandered around and explored
Day 10 Venice – Grand Canal Vaporetto ride up & back, Rialto Bridge. Evening – Orchestras St. Mark’s Square
Day 11 Took Alilaguna boat from San Zacarria-Jolanda stop to Marco Polo airport. 1 hr 10min
Flew home
I would do it all the same again except maybe change the Sienna day trip to a biking Lucca daytrip, or do 3 nights in Florence, and 1 night in Cinque Terre to have more time there. CT was so beautiful, and the lovely mountains, ocean and nature were a refreshing change from all the city time. Tailor your trip to fit your interests. Hope this helps!