Mozart

First, what is the "perfect setting" for you? Concert hall? Church? Park?

Second, Mozart is most closely associated with Vienna and Salzburg in Austria and Prague in the Czech Republic. Unless there's some special Mozart-themed event, you are unlikely to find a concert in Germany solely devoted to the man. Look for flyers in the larger cities, though. You may find something along the lines of what you seek.

Now, if you wanted to experience Beethoven, Bonn (about 40 minutes northwest of Frankfurt by ICE) usually hosts some-Beethoven themed events. But this city doesn't see the steady flow of tourist traffic that you might find in, let's say, Salzburg, so you probably won't find a regular cheap concert rotation like you might in some of the above cities.

Here are two good sites to help you:

http://www.music-opera.com/en/
http://www.classictic.com/en/special/classical-concerts-in-european-cities/198/

not at all on your route, but if you want to sit in one of Europe's grandest opera houses, in magnificent box seats, surrounded by locals as opposed to tourists; then make a detour to Budapest. Or fly to Moscow for a night. Air fare in Europe can be pretty reasonable.

Probably Munich is the place that has more concerts to offer; Bayerische Staastoper (with some secondary venues), Münchener Philarmoniker and Bayerisches Rundfunk Orchestra offer concerts and opera evenings of the highest quality, so you can begin looking at their programs.

I wouldn't neglect also cathedrals and major churches, that in the German area have the tradition of accompanying High Masses with chorus and orchestra; for example, on May 14th at 10am the Munich Dom will have a service with Mozart's Mass KV 275 performed by full choir and orchestra.