We just came back from our 6-day Northern Italy trip. It's also y first time in Italy.
We started in Lake Como. You can do a train trip from Milan. I haven't been there, but we decided to skip it because it didn't attract me as much as the other locations.
Day 1-2 - Lake Como (Bellagio) I was happy we visited this touristy place off-season. I believe you're coming in April, it's still off-season. But like what other reader said, spring is tricky. We visited when it was so cloudy. Though we can still walk around, I think I would have enjoyed the sights more with the sun.
Day 3: Verenna - I love this lake village so much!! It just has the vibe I was looking for in Lake Como. We hiked to the castle and the views were just phenomenal. Also, their gelato!! La Paserella - is something you can't miss if you're into ice cream.
Day 4: Bergamo - It's pretty, but I would skip it next time.
Day 5 - Verona - I wish I spent more time in this city!! It has the old medieval vibe I was looking for. I got the Verona Card (https://veronacard.info/) and normally, city passes are not worth it, but this card is 100% worth it! Everything in Verona is walkable.
Day 6 - Drive Back
I haven't seen Florence/Cinque or La Spezia, but I highly recommend Varenna and Verona. And spend 2 days in Verona. Take some time to enjoy the cities themselves and not so much on tours.
Happy trip!