Six weeks would be a great amount of time!!! The good news is that you can't possibly choose a "wrong" place to go in Italy.

Since you say you are going to Milan, be sure to reserve that Last Supper visit well in advance, or you may miss out. When my partner and I were there in May, we got to see a wonderful performance at La Scala. Highly recommended.

Lake Como was an easy day trip from Milan.

For Venice, if you stay longer, you have a better chance of seeing the places where the residents hang out, as opposed to the tourist spots.

We stayed in Airbnbs in Milan, Venice, and Bologna. All were excellent. I prefer these to hotels for the cooking amenities that they offer.

It'll be terrific. ENJOY!