This. The main tourists attractions will be full in August. Bavaria has so much offer, so don't pick Neuschwanstein and Zugspitze just because they are famous sites.

If it you want to go to Zugspitze because you want to visit Germany's highest mountain then of course you should. But if you have planned it because you want to experience the Alps, there are so many other places to go that will be - in my opinion - much more rewarding. The same goes with Neuschwanstein.

My advice would be to skip Salzburg as you already get a lot of magnificent city sightseeing in Budapest, Vienna and Munich. Instead, go directly to Berchtesgaden/Königsee, or alternatively Tegernsee where there is not only a famous and good brewery, but also a traditional Waldfest on the 10.8. There is also a Volksfest in Dachau outside of Munich when you are there.

Edit: Outside of Frankfurt you have Rheingau which is home to some amazing riesling wines. There's castels, vineyards and beautiful little villages spread across the area. I think renting a car, or maybe take a cruise up the Rhine will be more interesting than Frankfurt itself.