I spent 2 nights in MIlan before my BOI in Oct 2022. I stayed in a hotel where I'd stayed before because I like it, the staff and the area, lol. It is Hotel Duca di York and is near the Duomo. I'm a solo traveler so no experience with apartments in Milan. It took me about 30 minutes to walk from there to the Last Supper venue with a little sidetrack to see some ruins, lol. I also visited the Duomo with the rooftop access and went in to the Pinacoteca Ambrosiana which is literally across the street from the hotel. They have the original cartoons Raphael drew when he was planning his fresco in the Vatican Museum of The School of Athens. I knew we'd be going to the Vatican Museum and thought it would be interesting to see this planning step.
The Last Supper tickets need to be booked ahead as soon as they open for your time frame so go to the website to get a feel for it. I booked the 930 English tour thru the venue for an extra 8E and it was excellent. You are only allowed to stay in for 15 minutes and having the guide explain the fresco before and during was really helpful to me.
BTW, I suggest you download the train app for your ride to Varenna. I used the TreNord app and it was really easy. I bought the ticket right before I walked out of the hotel to go to the station.
Also if your group is up on ApplePay or GooglePay, that is good. If not, I suggest they start using whichever their phone supports. I used ApplePay all the time on my BOI. The only time I needed cash was 2 hotels where I'd had drinks/wine and they wanted cash instead of a card.