Mid-week destinations between Munich events

Seeing as you don't mind travelling some distance, research London. I have nothing good to say about Milan. Florence might not meet your art requirements in terms of the period you are interested in but I'm no expert when it comes to that.

I would take the train to Innsbruck, then Florence and if you have time, Rome. Then take the night train back to Munich from Rome. It's an over night train so you could save a hotel room.

Five days in Milan wouldn't please me; I don't see it as having five days' worth of sights, though a day-trip to Bergamo would help. Perhaps consider Turin instead; it sounds much more engaging to me.

I suspect many people would place Brussels farther down the list of Belgian cities than #2--but I haven't been there myself.

Farther east I'd suggest Warsaw or Kyiv as an option, especially if you have an interest in 20th-century history, but both have good art museums. For that matter, Gdansk, though not terribly large, could be considered due to its two excellent and time-consuming history museums (WW II and the Solidarity Center).

Or how about the combination of Zagreb and Ljubljana, though it might be a push to fit them both in. Zagreb has a lot of art museums. They are less than 3 hours apart by train or bus.

How about 2 nights in Milan and 3 nights in Florence?
I saw The Last Supper on a walking tour with The Walks of Italy. We explored the historic district and ended with a rooftop climb to the top of the Duomo with magnificent views.

On my own, I toured la Scala Museum, I tried too late to get a ticket for the opera there but the Museum is fascinating! Highly recommend.

Florence, of course, 3 nights for your schedule will be overflowing with possibilities for sightseeing!
Enjoy, I vote for Milan and Florence for your 5 nights.

I vote for Poland--my on a whim trip there in 2015 was one of my most favorite, and I'm about due for a return. I easily occupied myself for 4 days in Krakow and that included a day trip to Auschwitz, also Schindler's factory, the ethnographic museum, Wawel Hill and the Kazimierz district, plus daily walks around the main square. I also spent time in Warsaw, about 2.5 hrs by train from Krakow, and the National Museum has some fabulous art from my favorite era, in Polish it's called Mloda Polska, essentially the Art Nouveau/Secession years elsewhere. Other towns near Krakow that I would see upon a re-visit are Czestochowa and Wroclaw. Poland is cheap, beautiful, full of dark history, and fabulous :)

I'd go to Slovenia and Croatia. You can take a train to Ljubljana, stay 2 nights, another train to Zagreb, 2 nights, bus to Plitvice Lakes Park, and back to Munich easily.

If you plan on going to Italy, check out Air Dolomiti. They have daily flights between MUC and many cities in Italy such as Florence, Milan, Verona, Venice, Pisa, etc.

The only way to see Plitvice Lakes National Park these days is to spend the night before the park visit in or near the park. Don't try to handle it as a day-trip from Zagreb. The park is slammed by day-trippers to be extent that it seriously degrades the experience.