All of the day trips below can be done as a day trip in Munich. All of them are also offered as regularly scheduled tours from tour operators in Munich.
Neuschwanstein is a 19th century fairytale castle built on foot hill right up against the Alps in southern Bavaria. It is the most visited tourist attraction in the country and one of the most stunningly beautiful places you can visit in Germany. Nearly all tour companies in Munich offer day tours to Neuschwanstein which is a full day trip and you will want as much time there as possible so I would strongly advise against taking the shortest tour or any tour trying to offer side trips as there simply isn’t enough time to enjoy Neuschwanstein if you do.
Salzburg is a stunningly beautiful city just over the border into Austria. Some know it as the city of music as it is where Amadeus Mozart is from as well as the setting for the famous Sound of Music. It has a medieval castle, Baroque palaces, top art museums, and top shopping in a very small area.
Augsburg is the most historically significant city in the region. Having been founded by the Romans in 15BC, the home of the wealthiest family in Europe during the Renaissance, and the center of the debate during the Reformation, Augsburg is a gem of the Romantic Road. Located just 45 minutes from Munich, it is the less visited, but most rewarding of day trips from Munich.
Nuremberg is famous for two major periods of its history: the 1st Reich and the 3rd Reich. As a free imperial city (like Augsburg), it was independent for most of its history and widely considered one of the most important cities in the empire. During the 3rd Reich it was known for its massive rally grounds and later the infamous Nuremberg trials.
Dachau is the site of the first concentration camp set up by the Nazi government of Germany in March of 1933. It remained operational until the very end of the war. Although it certainly is not what many imagine themselves going to while on vacation, it may be the most important day trip you make.