It's my second home so I can probably answer some questions. I was there this Christmas and New Year and my main problem was the air pollution - it's not Beijing, but there's never any wind to drive the diesel gases away and when it happens to be foggy (rare) it's quite unpleasant. However, everything else about the city compensates amply.
The area within Palazzo Fava, via Marsala, Piazza Santo Stefano, Piazza Galvani and Piazza Maggiore is probably the most photogenic, with some of the better places to eat around the old market shops in via degli Orefici and Clavature.
The church on the hill is best left alone as San Luca only looks good from afar. Santo Stefano however, will repay many hours given that it is seven churches in one. Much might depend on where you're staying but generally events are well advertised:
http://www.bolognawelcome.com/en/home/live/events/complete-calendar/The largest collection of my shots from Bologna is probably this one.
https://www.flickr.com/photos/sandeha/albums/72157626573574759 I didn't make it to the Frieda Kahlo exhibition as the queues were really long but I saw an exhibition of Robert Capa's two years in Italy which was brilliant. Neptune is currently shrouded off for restoration work, but this giant character was burned to the ground in Piazza Maggiore on New Year's Eve. There's always some fun to be found around the main square.