That is a tough one. We lived in Munich for 3 years and it is a wonderful city and a great base for day excursions. You are staying near Salzburg on a farm for three days. (will you be in the Obersalzburg?). So, consider balancing that with the 3 days in Munich, explore the City and use it as a base for an excursion or excursions. When we had visitors we almost always took a day excursion to Neuschwanstein and Linderhof or Wieskirche. There are many other options for excursions outside the City. You could rent a car and experience driving the Autobahn to Garmisch, and/or to Oberamargau - my wife says a "must see".
I am suggesting you spend the time in Munich - it is a charming City and there is so much to see and do (Marienplatz, Deutches Museum, Englischer Garten, Nymphenburg Palace, many biergartens, art museums (Pinakothek) and ... depends on your interests. - Also great restaurants. But, if you decide one day you want out of Munich, jump on the train for a day in Nuremberg. Or being City dwellers, if you want more country for a day - you can hit the country-side quickly by train, car - or even bike.
And remember - if you are traveling in a few weeks, you will be coming close to Oktoberfest. It starts September 20 this year. Have a great time !