Palermo to Bologna – which cities to visit in between?

Is this your first time in Italy? If not what have you seen before?
I hope you realize your question is very broad. There are a tons of choices within the 600 miles segment you want to cover. Your trip is also very crazy. Sicily alone has a plethora of places to visit that can easily keep you busy for at least a couple of weeks, yet you plan to see only Palermo for 2-3 days.
The distance covered is so great (I’m not even sure you realize how great it is) that you should fly from Sicily to whichever destination you need to visit before Rome (for example Naples).

Ditto what Roberto said--we need some more info from you before making suggestions.
My first thought was why you were not seeing anything else on Sicily. You have to decide first if you want to see more of the island, then fly to Rome, or if you do actually want to take along train trip and stop en route (in which case I would look at the train route and research some of the cities where it passes through).
Have you made your list of what you want to see in each place? You could easily spend more time in Rome and Bologna, but Florence would make an obvious stop in between.
The one certain thing is that the possibilities are endless.

I can appreciate both replies so far. Yes I guess it is a bit crazy in a way. We wanted to see a bit of Sicily but my sister who is with us wanted to see Rome as well. And she is only with us for a couple weeks. So I thought we'd fly into Palermo, spend a few days there, perhaps hit one other city in Sicily for 2-3 more days, then ferry/train maybe up to Naples for another 3 days before going to Rome.

From Rome we'd catch another train to go to another city or two before arriving in Bologna, where we would fly out.

The high speed train is about an hour from Naples to Rome, so I was hoping we could use the high-speed for our entire travel within Italy, hitting cities along the way.

The itinerary is very broad, yes. We will only get to hit a few cities within this large stretch.

In the past we've visited Florence, Venice, Rome, Cinque Terre and Nice

Between Rome and Bologna I would make Orvieto one of the stops. Ravenna would be another, but it would be a diversion from Bologna, not right on the way.

Or you could go Rome—-Spoleto—-Ravenna, all linked by Frecce train (FA8854) and then regional train from Ravenna to Bologna. Which has some advantage in terms of arrival at Bologna, as the Regionale trains arrive at street level. The Frecce trains all arrive deep underground, and finding one’s way out of there to the correct exit for central Bologna is not easy if you are not prepared.