Dividing days between Munich, Salzburg & Vienna

As you are classically trained musicians ( as am I ) and given your dates , this isn't enough time for all you proposed plans . The first day , especially coming from SF , will be rough due to jet lag , and the day you leave is only going to the airport for your flight . With 8 full days , I would skip the day trips , and Salzburg as well ( even though Im quite fond of it ) three full days in Munich and the balance in Vienna would be best . In Munich , you may find performances by The Bavarian Radio Symphony Orchestra ( Usually at The HerculesSalle in The Residenz ) The Bavarian State Opera at The National Theater , is also worth checking out . In Vienna , the premier venue is The Muskverein , home of The Wiener Philharmoniker , and many visiting orchestras . There are numerous music focused sites in Vienna , among them The Beethoven Museum on Probusgasse in Heiligenstadt in the north end of the city . The Vienna Zentralfriedhof ( central cemetery ) has a section where numerous composers are buried . I spent two weeks in Munich and two weeks in Vienna this past Autumn , ( not my first visits ) and as always , it's never enough . Numerous great museums in both cities, so choose according to your interests . While in Vienna , I always make a visit to the cemetery in Grinzing to pay my respects to Mahler , who is buried there with one of his daughters .

We flew into Munich and flew out of Vienna. You could have one or 2 nights in Munich, 3 or 4 nights in Salzburg, and 3 nights in Vienna.

In Salzburg we really enjoyed the Fortress Concert in the Golden Hall. It was a highlight of our trip and worth flying across the ocean for. It was very professionally done, and included 1 piano, 4 violins, 1 cello, and 1 viola. The concert included Mozart, Strauss, Hayden, and Vivaldi. The ambiance in the Golden Hall was wonderful. We did not do the dinner.

We saw the Sound of Music sites on our own, walking to most of them. Take the Monchsberg lift up for great views,, walk along the path to the Hohensalzburg Fortress. On the way down stop at the Nonnberg Abbey where Maria was in the convent and which is the real place where Maria and Captain Von Trapp were married (not in Mondsee as in the movie.) At Mirabell Garden you can see the Do Re Mi steps, the Pegasus horse fountain, and the Dwarf Garden with the dwarf statue with the eyeglasses from the movie.
You can cross the Mozart Bridge from a scene in the movie. Stop at the catacombs and gravesites at St. Peter's Church cemetery which was used as the Hollywood model for where they hid while escaping. If you take a bus ride to Schloss Hellbrunn you can see the Sound of Music gazebo which was moved there. The trick fountains there are interesting also.

The Mozart Residence Museum in Marketplatz in Salzburg is very worthwhile.

In Vienna be sure to see Schoenbrunn Palace and the Gloriette Pavilion and gardens.

This sounds like a great trip!

Does opera count as classical music? Architecture and music converge at the Weiner Staatsoper. At a minimum, tour the building, but I believe attending a performance would be more rewarding. Just be wary of the Mozart impersonators out on the street.

Classical music events:

Salzburg
https://www.classictic.com/en/sitesearch/?search=Salzburg

Vienna
https://www.classictic.com/en/sitesearch/?search=Wien

I agree with Steven about arrival day. You need to settle in on your first day which is similar to a business day and end it with a nice meal and hit the ground running after your first night.
The next morning store your luggage at München Hbf and take a direct train from Munich to Dachau (15m). You don’t have time for Mauthausen and is best by car than train since it requires a transfer.
Munich is a great transportation hub but the city itself isn’t the best that Europe has to offer. I say after your first night in Munich go to Salzburg and sleep there for two nights (2h by direct train).
From Salzburg take a direct train to Vienna (2h 30m) and spend the rest of your nights there, you shouldn't be bored but if you are, take a day trip to Bratislava (1h) by direct train and explore the old town.

Disclaimer: I have been to Vienna and Salzburg but only to the airport and train station in Munich. I would cut out Munich to have more time in the other two. My favorite thing in Salzburg was seeing a piano that Mozart played-it was in one of the Mozart museums.

What you saw was the early forerunner of the piano we know today . Its at The Geburtshaus https://en.wikipedia.org/wiki/Fortepiano

We were in Munich, Salzburg and Vienna in Oct.
In Salzburg we did the concert at the Fortress without dinner. It was very enjoyable. I am not a classical trained musician but I do play the piano and violin. The space is small and intimate and I like watching the musicians playing and much as hearing it. There are a lot of Sound of Music places you can visit in the city. Mirabelle Palace, the dwarf statue garden, St Peter's cemetery was the idea used for them hiding in the abbey behind tombstones, Nonnburg Abbey are all places in the city. We did take a bus tour, about 3 hrs. to the church where the wedding was filmed, the lake were Marie and the children fell in and the back of the Von Trapp house (in the movie), the lane Julie Andrews walked down to get to the house. The tour was fun and we learned a few things.
In Vienna we were there on a Sunday and went to the Augustinerkirche, the church of the Hapsburgs. At 11 AM they have a mass by either Mozart or Franz Schubert with orchestra and choir. It is about an hour and a half, very crowded so get there early. It was great. They ask for a donation. Also the hearts of the Hapsburgs are kept in a crypt in the church although there bodies are in a crypt at the Caphucine Church in Vienna. We saw both.
We spent 4 days in VIenna, 3 days in Salzburg and 4 days in Munich.

A couple of days late to the party, but here are my thoughts...

Munich

• 2 nights
• If seeing a Nazi concentration camp is important to you, I would consider Dachau over Mauthausen. It's proximity to Munich is much better than Mauthausen's proximity to Vienna. If you choose to go to Dachau, you may want to add a night in Munich. Better yet, skip both and save your concentration camp experience for a future trip to Krakow from which you can visit Auschwitz.
  

Salzburg

• 3 nights
• I like Salzburg a lot
• I am not a musician, but I have a season subscription to the local philharmonic and regularly jump over to another city near me to see its symphony play. I found the fortress concert top notch.
  
• Nature scenery? Go south to Königssee near Berchtesgaden. It's a beautiful lake. Catch the electric boat over to the Salat stop, walk the short distance to Obersee, snap your iconic picture of a small building on Obersee, hike along the right side of the small lake to the other side, ascend to a gorgeous alpine meadow surrounded by mountains (and shared with cows), and then visit Röthbach Waterfall at the far end of the meadow. Return via the same route, stopping at the snack hut for some fresh-from-the-cow milk. I haven't been to Wolfgansee, but I can't see how it is possible that it could complete with Königssee. Nearby is the Jennerbahn, which can take you up to an altitude of about 1800 m.
• Off the beaten tourist path. Stadt:bibliothek Salzburg. The city's main library in the new town. Building that looks like a dinosaur. Shockingly red carpet. Panoramabar -- coffee house and reading room in the head of the dinosaur with great views over Salzburg, including views of the fortress in the distance. Coffee house employees are adults with developmental disabilities who are learning to work in the food industry.
  -The nearby ice cave (Eisriesenwelt) is awesome.
  
• I found the Mozart Geburtshaus more interesting than the residence. You get to stand in the room where Mozart was born... how cool is that?
  

Vienna

• 4 nights
• A concert at the Musikverein is super cool. A concert hall built by the Habsburgs would have to be great, eh? It's still considered one of the best performance halls in the world.
• If you have an interest in history, the army museum ("HGM") is superb. Excellent, excellent, excellent World War I exhibit, including the car in which Archduke Franz Ferdinand was killed, along with the clothes in which he was killed -- you can see the bullet hole in his shirt! A picture of Gavrilo Princip rests quite literally on the floor. The WWII exhibit? Poor.
• I find the Augarten pretty fascinating. It's an enormous park with garden patches, flowers, Austrians being Austrians, and... oh yeah... Flaktürme... concrete WWII anti-aircraft towers that are so massive they can't be destroyed.

Weighing in to vote for just two nights in Munich.

Ditto the comments above about Koenigsee:
“ Nature scenery? Go south to Königssee near Berchtesgaden. It's a beautiful lake. Catch the electric boat over to the Salat stop, walk the short distance to Obersee, snap your iconic picture of a small building on Obersee, hike along the right side of the small lake to the other side, ascend to a gorgeous alpine meadow surrounded by mountains (and shared with cows), …stopping at the snack hut for some fresh-from-the-cow milk. … Nearby is the Jennerbahn, which can take you up to an altitude of about 1800 m.”

We did Munich, Saltzburg and Berchtesgaden and the above was the best part of the trip. Easily a day trip from Saltzburg. On your way you may want to stop at the summer luge run about half way in between. Very fun even for adults.

Your best scenery will be a couple of hours south of Munich in the Austrian Alps. That's around Innsbruck. It can be reached by train.
As musicians, you may be in for a treat. Both Salzburg and Vienna are great cities for music. Concerts can be easily found online.
I personally have never taken a Sound of Music tour, but they are available.
Hallstadt is a good day trip from Salzburg--probably better than hauling all your luggage and staying at a hotel there.
If you're into WWII, by all means stop at the Mauthausen train stop. It's an uphill walk to the facility, but it's a pretty important travel sight for those that have never been to a "work camp."
All great cities are worthy of a 4 day minimum visit. I would say 4 days Munich, 4 days Vienna and Salzburg with what's left.
You can see what tours go to on TripAdvisor.com for any given city.

Late to reply, hope this info is still useful.

If it were mine, I’d spend the time in Salzburg and Vienna if you’re big classical music fans. Munich has about a weeks worth of things to do, but the other two cities are ground zero for classical music.

Salzburg has both the Mozart Birthplace (excellent) and Mozart Residence (it’s okay, though a short visit). If you’re going to do a Sound of Music tour, the city will likely take two days without day trips.

Vienna has loads of composer residences: three for Beethoven, two for Schubert, and one each for Mozart, Haydn, and Johann Strauss. They’re more akin to the Salzburg Mozart Residence, but interesting enough. You will also likely want to go to Zentralfriedhof, where many major composers are buried: graves for Beethoven, Schubert, Brahms, Von Suppe, and Johann Strauss father and son are located within steps of each other next to a memorial for Mozart; and Gluck, Salieri, Wolf, Schoenberg, Ligeti, Zemlinsky, and Pfitzner are also buried in that cemetery. There are also scads of museums, palaces, churches, parks, and an amusement park (the Prater), plus you access parts of the Vienna Woods via city bus if you want to hike. The city can keep you occupied for the better part of a week if you’re thorough.

If you're in Vienna on Sunday, be sure to attend the church service at the Augustiner Church(Part of the Hofburg Comple)-the music is sublime.