Milan

When is your trip? Hotel rates can fluctuate with conventions and whatnot in town.

Did you look on booking.com for your dates?

The London Hotel -- yes, there was a hotel in Milan under that name -- offers budget yet comfortable accommodations. I do not know if it is still operating. I was there in 1994.

Search results for “Milan hotels” past 2 years
https://search.ricksteves.com/?button=&date_range=2y&filter=Travel+Forum&query=Milan+hotels&utf8=✓

We enjoyed a 2 night stay at Hotel Duca di York
https://www.ducadiyork.com/en

Last Supper tickets official site
https://cenacolovinciano.org/en/

Duomo tickets official site
https://ticket.duomomilano.it/en/

Have you considered air b n b? We were there a few weeks ago with a great apartment just minutes from the duomo for about $200 per night , maybe even less. For last supper tickets the official website is cenacolovinciano.org they release tickets every 3 months so I was able to secure tickets in April I believe for our visit in July. For Duomo tickets we were able to get them the day before. There is a museum right next to the duomo where you can buy tickets to the duomo which includes tickets to the museum and they have a QR code that you can scan to buy tickets as well.

Look at Antica Locanda Leonardo very near Cadorna Station and “The Last Supper”. This hotel has a garden, very quiet.

We just booked a nice apartment in the Navigli district for 5 nights=$868 Canadian. AirBNB
More affordable accommodation is out there.
As far as the tickets...I'm also looking for that information.
Have a great time in Milan.

Lancaster Hotel was nice. We stayed there for 2 nights in June 2022, at the end of our trip to the Cinque Terre. It was clean, comfortable and a short walk to the Sforza Castle via a nice park.

We stayed in Ibis Milano Centrale. $135/night.

Big cities are expensive.