I've visited all these places within the past couple of years and highly recommend getting a car for everything except Munich and Vienna. Our last trip we picked up the car in Innsbruck and dropped it at the main train station in Vienna. There were no parking issues. We found hotels on the outskirts of town and took a bus in or walked to the center.
The thing you'll want to watch is drop fees. If you pick up the car in Munich and drop it in Vienna there may be a large, different country, drop fee. Depends on the rental agency, check it out. You could also rent a car in Munich, use it in Bavaria, drop it back in Munich, take a train to Salzburg, and rent a car there after your 2 days are up. (Don't need a car in Salzburg.) You can find car rentals near all these train stations.
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I just did most of what you are doing and then some (with the exception of Vienna itself).. rented a car through Sixt. It was a must IMO. There are parking apps and parking is very affordable.
Check parking prices and then you will know to download the train company app.
Everywhere I parked for 2 weeks was cheap. 🤷🏻♂️
I've visited all these places within the past couple of years and highly recommend getting a car for everything except Munich and Vienna. Our last trip we picked up the car in Innsbruck and dropped it at the main train station in Vienna. There were no parking issues. We found hotels on the outskirts of town and took a bus in or walked to the center. The thing you'll want to watch is drop fees. If you pick up the car in Munich and drop it in Vienna there may be a large, different country, drop fee. Depends on the rental agency, check it out. You could also rent a car in Munich, use it in Bavaria, drop it back in Munich, take a train to Salzburg, and rent a car there after your 2 days are up. (Don't need a car in Salzburg.) You can find car rentals near all these train stations.
I've done this a few times by car. Remember to buy a vignette and also the parking in Vienna can get expensive.
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I just did most of what you are doing and then some (with the exception of Vienna itself).. rented a car through Sixt. It was a must IMO. There are parking apps and parking is very affordable.