Munich changes the tone of the trip. The streets are wider, the food is heavier, and the Alps sit close enough to be a plan rather than a hope.
Day 5: Arrive and Reset
After yesterday's long drive, schedule nothing. Check in, find dinner close to the center, and save the walking for tomorrow, when the city is fresh and your legs are too.
If you are not driving, this is also the moment to work out the next three days, because the day trips are the part that needs booking rather than deciding.
Stay in the center rather than out near the airport. You come back to that room every evening, and the walk to dinner matters more than a shorter taxi at the end of the trip.
Day 6: Marienplatz and the Residenz
Marienplatz is the square to start from, with the Old and New Town Halls facing each other across it and the red roof of the Frauenkirche a few minutes away. From there the Residenz is the interior worth paying for: room after room of it, and a collection that explains what Bavaria was long before it became a holiday region.
Spend the afternoon in a beer garden instead of another museum. That is the local order of things, and it also keeps you fresh for the castles tomorrow.

Navigation is easy once you can see the Frauenkirche's towers, because the center is compact enough to cross on foot.
If you want the center explained rather than walked, a Munich tour with a guide covers it in a morning and leaves your afternoon alone.
Day 7: Neuschwanstein and Linderhof
Both of King Ludwig II's castles stand in the same stretch of the Bavarian Alps, so one day takes them together. Neuschwanstein is the one on the posters, built high above a valley with the mountains behind it. Linderhof is smaller, stranger, and the one that surprises people, with an artificial grotto and a miniature lake on the grounds.
Book the castle entry before you go, because the day is long and the driving is the part you cannot shorten. Coach trips out of Munich do both in a day and put you back in the city by evening.

One warning from experience: pick the castle you actually want to go inside and see the other from outside. Two interior tours in one afternoon is a lot of stairs for the reward.