Three weeks might be a stretch for Ravenna; it would be very slow travel indeed. OTOH, you could do day trips to Bologna and Ferrara by train and explore by car the coast or the area south of Faenza and Forli (I understand Brisighella is nice but I've not been there).
As for Bologna, I would avoid the area around the main train station and the smaller train station to the east (primarily due to noise). The main street from the train station to the piazza maggiore (Independence?) is (or was) very noisy so I would not want to be directly on that street. Fourteen years ago I was told to avoid the area around the theater (sketchy at night), but I don't know whether that assessment is still valid. Bologna has (or had) an excellent bus system, but I still think it's best to be within walking distance (which would vary for different people) of the main things you want to see. I would not venture outside the ring road. However, I did stay several blocks outside to the south of the city 14 years ago and that was a very nice area with a big park close by. I usually took the bus into the center each day and did not return to the apartment until late afternoon. But the knees were better then
.
I've never been to Parma, but I imagine it would be a good place to stay for a while. It has been "on my list", for many years. However, it's a little difficult to get there by bus (I can't do trains with luggage). It has good train service to Bologna (about an hour, I think) and I've always wanted to explore the area south of Parma. OTOH, I don't think there are many sites in Parma itself. I would also consider it for a day trip from Bologna.
Yes, Lucca deserves it's own trip, although it seems to get a lot of one-day visitors. I spent a week at this place (
colle verde) many years ago with my sister and daughter - rustic digs but fabulous area; you would definitely need a car. You could also stay in Lucca (I recommend within the walls) and take side trips by train/bus (or if you are very brave by bicycle).