10 nights- I'd stick to 3 locations. Each location change eats up half a day.
(actually is it really 10 NIGHTS? do you arrive in Italy on the am of 4/12?)
Easter is April 20- just so you are aware of that.
Palm Sunday is 4/13- that wil be a busy day in towns.
Some restaurants will be closed on Easter, reservations will be a must.
How many nights do you think you'll want in Milan? What are your must dos there? I'd say 2 minimum to see Last Supper and Duomo (if those are on your list) Last Supper tix go fast so you will have to stay on top of that
Bologna is flat and what is nice is the porticoes- if it's raining or just too hot you can at least explore under cover. It's the foodie capital 3 or 4 nights- allows for a day trip to see the mosaics in Ravenna
Travel to Genoa from Venice will take 6-7 hours with change in Milan. IMO that's too far to travel on a short tip.
Travel to Turin from Venice is about 3.5 hours with change in Milan.
Assuming your flight is into Venice, out of Milan
Venice- 4 nights- that allows for a day trip to Padova
Train to Bologna
Bologna 4 nights- day trip to Ravenna
Train to Milan
Milan 2 nights- this will be Easter weekend