Looking for 3 week itinerary for Northern Italy

So- you are not considering beautiful Lake Como? I'd highly recommend that area.
Safe travels!

You have time to fit in a day trip to Lake Como. From Milano’s Centrale station take a direct train to Varenna (1h 15m) and explore this cute clean town before hopping on a 15-minute ferry to Bellagio to explore its lanes with stairs featuring high-end retail that is pleasing to the eye. You need a minimum of three nights for Milan.
You can take a direct train from Milan’s Centrale station to Monterosso (Cinque Terre) that takes 3h. Do you hike? I did from Monterosso to Vernazza which appeared to be easier than Vernazza to Monterosso where the views are supposedly better but the steps along the path are steeper. It's easier to climb up steep steps than down. You would need three nights to explore the Cinque Terre if you took this hike. If you add more hikes add an additional night per hike.
From Monterosso take a train to Florence’s SM Novella station that requires a transfer. If you connect in Pisa (1h 15m), you can store your bags nearby and check out the Leaning Tower and the Field of Miracles before continuing on to Florence (1h 15m). You need three nights for Florence.
To explore Tuscany rent a car in Florence and drive along the Chiantigiana (SR222) to Siena. After two nights in Siena drive to Pienza’s old town before stopping in Montepulciano and sleep there for two nights.
I’ve been to Bologna but only for a few hours so I can’t recommend anything but those who spend the night like it.

We did 3 weeks in N Italy. We did Milan, Ravenna, Padova, Turin, Pisa, Siena, Firenze. We spent 5 nights in Turin for a food-wine festival, so we could have done another city (Genoa? Cinque Terre?). 3 nights Milan, 4 night Firenze, 2 the others. Our interests are food, wine, and art.

Thanks all for the replies. Definitely have decided to get to Lake Como on our trip.
And we do enjoy hiking, but our knees, not so much! I expect we'll try to get in just one hike (on the easier side) while in Cinque Terre.

It looks like you already have a good plan, just need to play around with the train schedules to get the order right. The only time you would want a car is for rural Tuscany. I personally would not need four days in Milan, but it depends on your preferences. Four for Florence, a few for CT depending on how much hiking you will do, and about a week for the Emilia-Romagna cities sounds about right.
So curious about the biking trip--hopefully it takes in gorgeous San Bartolo park--I only skirted the area but it seemed so built up.

At end of May is cherry season. I live in Vignola, between Modena and Bologna, and is ione of the most important cherry district of Italy. You could visit Vignola by train from Bologna (there is a huge medieval fortress too) and enjoy an easy hike along the Panaro river and among the cherry orchards. Usually the first two week end of June there is even an harvest festival about cherries, if you will be in the area.
Near Vignola there is the "Rocca Malatina's rocks" http://www.parchiemiliacentrale.it/parco.sassi.roccamalatina/ . Is another very nice area where to enjoy nice hikes without be packed in the crowd of other parts of Italy.

I like Rickys suggestion. How lovely to bike through cherry blossom season in Italy. That means staying in Modena-lovely small, quite quiet city or Bologna-larger, lively and foodie. Or stay in Vignola and have the hiking too. OR? Sure you could also fit in Lake Como.

When you say easy hike in CT-hmmm-none of them that are open right now are a walk in the park so to speak. Lots of up, down, rocks and dirt. We loved it though.

To be honest, cherry blossom season in Italy (at least northern Italy) is between March and April (depending by weather). End of May and June is the cherry harvest season, where to enjoy and eat the fruit!
From Modena and Vignola there is a 30Km long bikeway created on the former railway. Completely plain and very easy. A perfect way to visit Vignola bikeing because is mostly far from the normal streets, so safe and quite. In cherry blossom season you pass through orchards with the white flowers, but when there are the fruit is better because you can stop along the route to directly purchased cherries from the farmers. When you arrive in Vignola you can continue following on the left side of the river and for 20Km the bikeway is pretty easy, before start to climb the hills. Is part of EuroVelo #7, the Norway-Malta bikeway. Or course you can do it hiking, if you prefer.
If you stay in Bologna you can easily reach Vignola by train. You can transport the bike on the train, because unfortunately in Vignola we don't have yet a bike rental.

Is this your first trip to Northern Italy? I only ask because your choice of Bologna, Parma Modena is curious to me and I would think a week is too long. We have visited friends who live in Bologna and I thought 3 days was too long. The Lake District is quite magical and with Milan as your airport of choice you could easily access Lake Maggiorie and Lake Como. But if Bologna, Parma and Modena are really calling you you could add Lake Garda to the end of the that itinerary and train back to Milan from there and get a lake visit in. OR three nights for Bologna, Parma and Modena and 4 nights for Verona and Lake Garda - either Milan or Venice are airports with easy access after that.

Oops- not cherry blossom time! Cherry eating time. Even better.

Bologna seems to be almost a love it or leave it. We were there for 10 full days, one a day trip to Modena. We would have stayed longer but our flight out was the reason to leave. We loved Bologna.

My husband and I are also going for 3 weeks at the end of April and beginning of May. We are going to:
- Milan (flying in and only for a day)
- Lake Como
- Dolomites (Bolzano via Verona)
- Venice
- Cinque Terre (via Bologna)
- Asti (wedding at Serralunga D’Alba)

We are only renting a car after Cinque Terre (maybe in Genoa) and driving it to Asti since there’s no train easily accessible to the wedding venue. We will return it in Milan before flying back home. All other travel will be done on trains.