I don’t know much about Munich. We flew in there in 2012 for my first trip to Europe. We spent 1.5 weeks with a private guide who drove us 6 family members all around Germany in a van, mostly looking at castles, but also a day trip River Cruise on the Rhein, a day in Legoland, a day in Wolfsburg, and then dropped us off in Berlin for a few more days. Everything was set up for us, and it was wonderful. Peter felt like family by the end, but I digress.
Anyhow, you are 2.5 hours from the iconic Neuschwanstein Castle, if that interests you. Looks like it can be a day trip you can do solo, though having a guide seems to be easier from what I googled. The Hohenschwangau is also right there… We are castle freaks in our household. Other may not be. But Bavaria is just so so so beautiful. You probably can’t go wrong anywhere.
Edit: I see Nuremberg is an hour away. I’d definitely add that to your list for Xmas markets. It’s on my bucket list.