Definitely Ravenna for the mosaics.

You can reach Florence in less than 40 minutes by train.
Don't miss San Luca in Bologna ( can take half a day).
We did not find a week too long...

another vote for Ravenna for a day trip.

Ravenna is fabulous. I don't think a week is too long in Bologna. I really enjoyed our 4-5 days there a couple years ago. Other than Ravenna I'm not sure of the distances to some of the other towns, but there are many interesting ones close by.

by train , one can reach Modena and Ferrara in less than 30 minutes
Verona and Ravenna about and hour and 30 min.
Venice an hour and 40 minutes.

Be careful about washing your nylons in the sink.

That's my experience with Bologna. In about 1967, back before panty hose, while I still dressed up for travel, I was washing my nylons in the hotel sink. I must have removed the plug too soon, or maybe there was no plug. Anyway, one of my nylons got sucked down into the drain. I was worried that I'd clogged up the drainage.

That's what I always think about when I see the word Bologna. I wish I'd gone to Ravenna.

Modena - take the bus (about 12km or so) to the Ferrari Museum. (Across from the factory and not an official museum).

The Maserati factory is also in Modena. There's also a great, old salumeria, I remember reading an article about Mario Batali visiting there.

Parma - Prociutto. Try La Greppia restaurant.

It may not have very many sites, but the best food in Italy comes from this region.

love bologna
love ravenna
love parma
love padova

you can't lose visiting any of these.... you will wish you had more time! it's not too long.

Check the news about the recent earthquakes in Emilia. I do not think Modena is a good destination right now because it is in the affected zone and has suffered significant damage, for example the historical clock tower has collapsed. Not sure if the Ferrari factory is already back to normal either.