Must see cities in northern/central Italy.

We spent a couple of nights in Verona and really enjoyed it. A very walkable city.

So, excluding Florence and Siena, of the cities I’ve visited between Venice and Cinque Terre, I would recommend Padua, Verona, and Mantua over Lucca. San Gimignano is great, but I think it would be a bit of a detour.

Depends on the pace you like to travel. Your current list is fine as is. I have avoided Cinque Terre so far but have been to the other places. I could spend weeks in Venice again! San Gimignano is one of my favorites. However, Lucca not so much. If you base yourself for a few days in Milan or Bologna, you could do some day trips to places like Ferrara, Mantua, Parma, Lodi, Spello, Assisi, and so many more. Orvieto and Urbino are jewels in central Italy, IMO. I generally avoid journeys of more than an hour and a half for day trips via public transportation. A car will definitely make things easier, but parking could be an issue (others here are more experienced with that). In the north, Milan gets a bad rep for being the financial and industrial center of Italy. I feel just the Duomo, Sant'Ambrogio, San Babila, and the Brera museum more than make up for it. You have so much to choose from in these two regions!

I enjoyed Mantova and Parma, and both are in train lines so no car needed. Mantova especially punches above its weight. Interesting sites for a smaller city, and would be good for a couple nights.

You could certainly fill 14 days in those places, so it depends on your preferred pace. Just look at the train system map to identify some day trips to fill it out. A car would only be of benefit for San Gimignano.
Tackle the “low hanging fruit” first by deciding how long to spend in Venice.

It would also be helpful to know where you are flying into and out of as well as your interests.

Assuming you're coming into Venice and and have 15 nights I would recommend something like:
3 nights Venice (minimum especially with jetlag)
3 nights Florence + 3 nights Siena (doing SG from Siena as a tour) and an overnight in Lucca on the way to CT
or longer in Florence and Siena, San GImignano and Lucca as day trips from Florence
2/3 nights in CT

This leaves you a couple days free at most. Bologna is an interesting large food-centri city on the way from Venice to Florence but there is also Ravenna for mosaics, Ferrara for old walled town and castle tours, Modena (from Bologna) for smaller food-centric town. As mentioned Verona and Padua/Padova are in the mix as well depending on what your criteria.
So it depends on your interests as what to add. Your itinerary seems to 'scenic places' so there is also Lake Garda - depending on month - or Treviso which is a little out of the way but might be worth it.

It's hard to choose wrong, have a great trip,
=Tod

Please check any plans with the Trenitalia train website, first, during your itinerary draft because some day-trips being suggested are more than 3 hours one way (although wonderful cities to visit!)

I’ve stayed in 50 Italian cities and never rented a car. The trains are very easy to navigate, and you don’t need to worry about ZTL fines & trying to find parking in the smaller cities on the edge of town.

Along the northern routes, my favorites are Torino, Asti (if you’re there for their Palio), Stresa, Bergamo, Cremona, Parma, Mantova, Verona, Ferrara, Ravenna and my #1 - Venice. If you’re dipping into Tuscany, you’ve mentioned Lucca. Also Montepulciano is very nice but easier to get to from Florence or Siena by public transportation, so you probably want to skip it unless you do decide to rent a car.

With your amount of time, I’d save the Umbria area and other regions for another trip when you can concentrate on them. Have a great trip!

”3 nights Venice (minimum especially with jetlag)”

Absolutely! Do not skimp on Venice. If you’re just there for 1 1/2 days, there’s a big chance you won’t like it because you won’t get beyond the crowded tourist main walking routes.

Hi, Giangilberto from Milan, I recommend visiting Ravenna, you can get there by either car or train.
For example, from Venice, there are both high-speed Frecciarossa trains and regional trains, you always have to change at Bologna station.
Ravenna is world-renowned as the capital of mosaics and for housing no fewer than eight Early Christian and Byzantine monuments designated as UNESCO World Heritage Sites.

rent a car - easy to drive in Italy. Orvieto in Umbria and about 2 hours north of Rome is my favorite hilltop town - great views, outstanding cathedral, St Patrick's well, great food and wine. Orvieto was used for the Pope when he had to abandon Rome and it reflects that.

Lots of wonderful small towns in northern Italy. IMO Lucca was boring, that includes the bike ride on the mound around the old town. Your choice….

Do not skimp on Venice! I would spend a minimum of 4 nights in Venice, and a 5th night would be golden. I would spend a minimum of 3 nights in the Cinque Terre. We loved staying in Manarola. Manarola is quiet in the early mornings. Daytrippers start arriving around 10AM. And the evenings are spectacular. Gorgeous sunsets, fewer crowds. The crowds start thinning out around 4PM.

We visited SG for a day; however, a night or two would be nice.

I know some people don't care for Lucca, but we really enjoyed Lucca. Stayed 3 nights. One of the best hotels of our trip. Beautiful churches, evening concerts, explore the piazzas, and take a bike ride, or just walk, on top of the walls. We loved our daytrip to Pietrasanta, a medieval town known for its sculptures, cathedral, and historic center.

We also enjoyed staying in Parma, if you want to add another destination.

Where are you flying into and out of? Milan is wonderful, too! The Duomo, with its rooftop tour is exceptional. Try to get tickets to see The Last Supper.