If it was me, then I'd look for two bases, one in each province (maybe that's your plan, and I didn't understand).
We've just come back from a first visit to Bologna, and were very impressed with the city. Looks easy to use public transportation from there. The interesting part of the city is actually not large at all - everything in walking distance - so even if you decide not to head out of town, you'll have plenty to see within easy reach. We spent four full days there. It's not very centrally located in the province - but this depends on what else you want to see in the area.
In Liguria : we've stayed in Levanto and really liked it. The train runs through the town. A beach, nice shops and eating places, plus a scenic location and a lively character make this an enjoyable place. Of course there's Genoa, which we also loved, but this city is less centrally located.
If you want to go a bit away from the more frequented spots (and have a car), then the mountainous area between Levanto and Piacenza is very attractive. From Levanto going north : the towns of Varese Ligure, Borgo Val di Taro, Bedonia, Bettola, Bobbio and Travo - very nice places with scenic drives between them. We hope to return there sometime.