We land at Rome and then want to go north by train - suggestions please

Perugia, Bologna, Torino
sorry but a 14 day trip and you visited 7 places (even with day trips) is a lot.
Why not spend a night or two in Rome?

Ravenna, the mosaics in Basilica San Vitale and Basilica Sant'Apollinare in Classe. ee Wikipedia which also has pictures. I visited last February. These are byzantine mosics that are incredible and look brand new, not 1500 years old. There are three basilicas to visit for this and one is a short bus or cab ride just outside of Ravenna, suppose to be the best one but I missed that one. the others are an easy walk from the train station, about 15 minutes if I recall. Its a flat town, easy to find things with a map in hand.

http://www.turismo.ra.it/eng/Discover-the-area/Art-and-culture/Unesco-world-heritage

the town is lovely and easy to walk, easy day trip from Bologna and Florence. From Florence - Fast train to Bologna is half an hour , then a regional to Ravenna is 1 hour.

Bologna, Torino. Then rent a car to explore the Poemonte.
Or Bologna , Verona, Lake Garda.. Then rent a car and head to Ortisei in the beautiful Dolomites.

Ravenna
Bologna
Ferrera
Verona
Cortina
Trieste

Fly out of Venice

I'd suggest having a look at the RS Italy guidebook or other reference sources to determine where you might want to go. There are endless possibilities, so it's difficult to offer many suggestions simply on "go north by train". It would help to have some idea on what you want to see or do on your trip this time?

Is there a possibility you could re-visit one or more of the locations you visited before, perhaps using them as a home base to visit other places? An example would be using Florence as a home base to visit Pisa, Lucca, Padova, Assisi or where ever.

More information would help.

if you're going north on the train, keep going. Milan to Bernina Express to Switzerland!