After traveling to Prague and Vienna in September would it makes sense to end trip in Munich? And if so how many days would you allow? Any day trips outside of the city that would be worthwhile?
Munich has tons of day trip opportunities so I'd give it as much time as you can - 2 days for Munich itself and however many day trips you want. You can day trip to: Regensburg, Passau, Augsburg, Ulm, Oberammergau, Garmisch-Partenkirchen, Fussen (for Neuschwanstein and Hohenschwangau). Endless possibilities depending on your interests.
Mid to late September is a very expensive time to stay in Munich with Octoberfest taking place September 17-October 3, 2022 and hotel prices inflated. Otherwise I would recommend staying 5-7 days in Munich with a couple of day trips. It would also be helpful to say the overall length of your 3 city trip. Perhaps going to Munich very early in September would help with hotel availability and prices. It really depends what your interests are but I never tire of a week or so in Munich.
I think I would consider stopping in Salzburg on the way to Munich, visiting Berchtesgaden from there.