There's a lot to unpack here.
Venice is not a good base to explore from because getting to the train station can be slow/difficult and you need to get to the mainland before you can even start to head to another city. Verona is a good choice but August is season there - operas in the Roman Arena and music in the old Roman Theater.
First off: Summer in Italy is both hot and high season. The idea of staying 3 different places for a month each becomes much harder in high season. Every place has its special days, conventions, festivals and so certain days are hard to book. And if your visit falls across that time you will be limited in what you can rent or it will be very expensive. Unless they are "money's no object" people mixing cities can help defray costs for what will be an expensive trip. Also because it is in season they should book ahead of time which will limit their flexibility but I wouldn't want to show up in Florence in September with no reservation and wing it trying to book a week plus.
I would advocate for breaking up the big cities and tourist sights with smaller and more out-of the-way towns. But smaller towns and really getting into conversations with Italians brings up the language barrier. English is relatively prevalent in hospitality in larger cities but can quickly diminish outside of those places. I remember one (older) study that surveyed Italians and 80% of them rated themselves as speaking "some English" but on 20% did when actually tested. Italians love to talk and they love it when people are really trying to learn the language but no understanding the simple conversations of people around you can be alienating after a while.
Anyway here is my 88 day blind swing at a schedule that mixes big cities, small towns, allows time for side trips and exploring.
It includes north south and some east, west as well.
Place (Alternate) Days
Venice 5
Verona 6
Malcesine 5
Bologna 7
Florence 10
Lerici (Chiavari) 7
Siena (Arezzo) 7
Cortona (Orvieto) 4
Perugia 7
Rome 10
Pescara 5
Bari 5
Naples (mixed with Salerno) 10
To be clear I'm not advocating they sit down and book this I'm just trying to illustrate what that many days spread between a bunch of different places might look like.
It sounds like they still have some large and fundamental questions to be answered but if they embrace it there's a real adventure to be had.
To them: Buona fortuna per la tua grande avventura,
=Tod