What to do in the rain?

The art museums - Pinakothek der Moderne for more 20th century stuff, “Neue” if you’re more into the 18th and 19th century artists like Monet and Klimt, or “Alte” if you like the older masters

Dachau is oddly a good rainy day trip

I thought this was a good article with ideas I wouldn’t have thought of:
https://boredinmunich.com/munich-in-the-rain-guide/

It won't rain all the time, but there may be showers every day next week.
And there will be a drop in temperature (from 75F today to about 50F) and possibly fresh snow on the Zugspitze.

If you want to go to the mountains do it today. If you want to sit comfortably in a beer garden, do it today.

It's best to get a good weather app. I use "DWD Warnwetter". The rain radar function shows when to expect a rain shower. One or two days in advance it gives you a rough indication, one or two hours in advance it's pretty accurate.
Thus it helps planing times for indoor and outdoor activities.