Advice for Itinerary (Rome, Florence, Tuscany, Cinque Terre)

I’d skip overnight in Pisa… just stop, check luggage-see the tower and head to Cinque Terre and stay in Vernazza.

Travel onward to Florence on arrival to Rome and move all your Rome nights to end
Eliminates a split stay and that 1 night wasted at airport hotel

I think the overnight in Pisa is fine since you want to visit both Lucca and Pisa that day
We enjoyed our overnight in Pisa -the builfings on Field of Miracles are stunning all lit up at night

For CT-stay in one of the 5 towns-not LaSpezia

Also-Florence needs more time -you only have one full day there since you have day trips planned
TBH I would skip Lucca and Pisa, neither are all that interesting or unique
Both Siena and Orvieto have more to offer

ETA
Ooops sorry missed Orvieto
Travel onward to Orvieto on arrival and spend first night there then to Florence

13 nights
Orvieto 2
Florence 4 with 2 day trips
CT 3
Rome 4

Rome can always use more time so if you can add a night give it to Rome

I agree with saving Rome for the end so you don't backtrack. I would go straight to Orvieto, spend 2 nights, as your arrival day you will not get to see much and appreciate it. Then on to Florence. If you want to see both Pisa and Lucca, I would stay in Lucca. It is a much more charming town. As for Cinque Terre, I would stay in one of the towns, not La Spezia. It is more of a port city, not a quaint village. Vernazza, Riomaggiore, and Manarola are my favorites. Monterosso is popular, but much more touristy because of the beach. Corniglia is a bit out of the way and not on the water, but you can still visit by train.

I did not do Orvieto.

We actually flew to Pisa and stayed overnight 1 night, which we actually loved. You have the entire town to yourself as most people are day trippers. We loved taking sunset pictures on a virtually empty Piazza de Mircoles. And then were up early to go to the Tower before crowds arrived.

We stayed 2 nights in Cinque Terre (above Monterosso). We were surprised to find that we wished we had stayed longer in Cinque Terre,

Orvieto is a great little town to visit but be aware that because you need to take the slow train both Rome to Orvieto and then onto Florence you'll spend at least 4 hours on the train (more depending on the available trains) versus about 1.5 hours from Rome to Florence directly on the fast train. Choose your trains wisely or you'll spend way too much time on the train for this leg.

You might think about training to Pisa, dropping off your bags, and then continuing to Lucca. This will add a little train time but will allow you to wander Lucca without worrying about your bags.

If you're spending time in La Spezia I urge you to check out the southern side of the bay. Take the bus to sleepier San Terenzo and you can walk along the waterfront to the more resorty Lerici with the marina and the castle on the hill. For the full tour there is the tiny CT like town of Tellaro and inland Sarzana just over the hill. These areas are touristy - all Italian beach towns are in the summer - but these are Italians on the coast for the season rather than day trippers.

Have a great trip!
=Tod