Trip to northern Italy in early October.

October can be lovely in Northern Italy but it is past the official season for hiking and higher elevation activities, so you may encounter limitations on lifts. We go to the Val Gardena every September without a car. Train to Bolzano, bus to the village of your choice. (We prefer Ortisei.) Once there, your lodging will give you a card for the bus system that will take you throughout the valley.

First, keep in mind that Milan has 2 airports. We have found Linate to be more convenient and often has lower fares coming from the US. Unfortunately, none are direct. Also, train travel through that region can be spotty so you may want to consider a car rental.

Consider the following for N. Italy: Around Lake Garda, Malcesine & Santuario Madonna della Corona. We enjoy the Süd Tirol region - especially Glorenza and the drive to Merano. Urtijëi is a lovely village. Consider some hiking around Lake Misurina.

Take the train from the Malpensa Aeroporto to Milano Centrale (45-minutes). I would spend a night or two in Milan and explore the city the day of arrival. The next day take a day trip to Varenna (Lake Como) and take Rick Steves’ self-guided walk before hopping on a 15-minute ferry ride to Bellagio for lunch.
To get to the Dolomites from Milan, you’ll need to depart from the Centrale station and connect in Verona’s Porto Nuova station. Total time takes 3h 30m.
Rick Steves’ recommends sleeping in Castelrotto/Kastelruth to visit Seiser Alm/Alpe di Siusi, the highlight of the Dolomites. You’ll need to walk from the Bolzano/Bozen rail station to the Bolzano Autostazione (bus station): https://www.google.com/maps/dir/Bolzano%2FBozen,+Bolzano,+South+Tyrol,+Italy/Bolzano,+Autostazione,+Bolzano,+South+Tyrol,+Italy/@46.4973352,11.3583651,18z/data=!3m1!4b1!4m14!4m13!1m5!1m1!1s0x47829e776e34b12d:0xb4b524bd7988513c!2m2!1d11.3582036!2d46.4967342!1m5!1m1!1s0x47829e7128ab7e93:0xd06aec8ff58a4798!2m2!1d11.3608468!2d46.4980067!3e2. The bus will take 1h.
The bus transportation between Castelrotto and Seiser Alm is 30-minutes. Rick Steves’ Italy guidebook (not the Best of IT) does a good job recommending hikes depending on your physical fitness level and other sites that are nearby.
You’ll then need to take the bus back to the Bolzano/Bozen train station and transfer to get to Verona (1h 30m).
The train from Verona to Vicenza takes 45-minutes and you can leave your bags at the train station in the left luggage area while you explore the city before moving on to Padua (30-minutes) where you can spend one night. The next morning visit the Scrovegni Chapel, but you’ll need to buy your tickets online before leaving home to avoid it from being sold out the day that you're there I believe. From Padua, take the train to the end of the line called the Venezia Santa Lucia station (30-minutes) and enjoy Venice before your flight home.

As Laurel explained, some areas of the Dolomites start closing down in October for a break, or even in late September. We stayed at a lovely little hotel in Santa Cristina (in Val Gardena, near Ortesei) the last night before they closed, on September 26, a few years ago. We were the only guests, until a couple of motorcyclists on tour arrived. They said they felt lucky to find a place that was open.

From Santa Cristina we went to the town of Tires to meet some German friends at a hotel that stays open until mid-October, and spent 3 more days hiking there. It was lovely—but we had a car. I don’t know if there is bus service to Tires.

https://www.seiser-alm.it/en/alpe-di-siusi/tires-al-catinaccio/tires-village/

Laurel and her husband have written an excellent guide to hiking around Ortesei. I have the original and it has been completely updated since then - available in Amazon

I find with Amazon UK, I'm sure that if you put in the info in the US Amazon it will be there:
https://www.amazon.co.uk/Walking-Italys-Val-Gardena-Dolomites/dp/B0851LV11G/ref=sr11?dchild=1&keywords=laurel+barton&qid=1624814806&sr=8-1

The deal with the Scrovegni Chapel in Padua is that even pre-pandemic you couldn't buy same-day tickets. It wasn't selling out at the time of my 2015 visit, but if they've had to lower capacity for health reasons, I guess that might be a risk.

Padua has a number of other sights in addition to the Scrovegni Chapel; I filled nearly two days there, but I do like walking around historic districts a lot.

You definitely don't have time to get a decent look at all the possible stops between Milan and Venice. If your taste runs to ancient hill towns, I'd recommend Bergamo. But ultimately you'll need to choose among The Last Supper and some big-city sights in Milan, lake villages and scenery on Lake Como, the hilltop upper town in Bergamo, the Dolomites, Verona, Palladian architecture in Vicenza, all that Padua has to offer and then Venice.