Vienna Opera early March, advise on 10 day itinerary to include Germany or Switzerland

Put Vienna (opera) at the end of your trip so you have time to get over jet lag.

Your wording implies you don't expect this to be your first and only trip to EU, so don't bite off too much where you will spend most of your time traveling from major attraction to major attraction. Instead, cut back and sight see in more depth.
Example: 5 days Vienna (one day to Melk), 3 days Prague, 2 days Budapest.

Or go for a drive. I much prefer travel by car for flexibility, especially in the Alps because the weather can go very bad. We plan two parallel itineraries, one for good weather (scenic mountain drives), one for bad weather (towns, cites, museums). Example: My Mother took a lifetime total of one trip to EU for the passion play. We were driving around Austria at the same time and met up with her tour in Innsbruck. Next day, her tour went to Zurich in pouring rain & fog-- never saw any mountains. We stayed in Innsbruck & went museum hopping. Next day, sunshine and we went back into the mountains.

March is not a good time to see the Alps because a lot of mountain roads are closed by snow, so forget Switzerland. If would be a good time-- no crowds-- to explore the Danube Valley (Vienna to Salzburg) with side trip no Chesky Krumlov or the Fussen Castles. See Krems, Melk, St Florian, Wilhering, Mauthousen Salzkammergut.

Linz & Munich are a waste of time.

Seriously consider flying Business Class.

I see that Turandot is scheduled for March 1, 5, and 9 at the Vienna State Opera. I suggest you first secure tickets for the date you want, then build an itinerary off of that.

Actually, the Alps are spectacular in the winter, and surprisingly, you have a better chance of clear weather then. It will be ski season, so the mountain towns will be busy. If you do not rent a car, you can go to places by train where cars can't go, and save your self from winter driving headaches. It is also expensive to rent a car in one country and drop it in another, since the car has to be shipped back to its home country before it can be rented again.

Flying business class? Sure, if you can afford it, but I can't, so I travel in the back of the plane. Suggest flying into Zurich and out of Vienna. For stops, start in the Berner Oberland region for at least 3 nights. It is kind of the go-to spot for scenery and ambiance, especially if you have never been to Switzerland. Lauterbrunnen is a good choice, but Wengen or Muerren will be on the mountain and pretty expensive as the skiers will have it booked up paying top dollar (or Franc). Still, take a look at it. These are car-free villages that can only be reached by train or cable car. Then train to Salzburg for a few days, then Vienna. All well connected by train. Train from Interlaken to Luzern is especially scenic going over the Brunig Pass.

Will you have 10 days in Europe, not counting arrival and departure days? I ask because if your count includes your days of arrival and departure, you actually have 8 days. Even with just 8 days, you could fly open jaw between Munich and Vienna - maybe with a stop in Salzburg, or see it as a day trip from Munich.

I would suggest that you buy your opera tickets as soon as your plans are set and the tickets are available. I regret not spending more money for better seats when we saw a performance in 2015 - it still sounded wonderful though.

We will definitely get the tickets first then plan around it. Thank you all for the suggestions.

Welcome to the forum!

In preparation for your first trip to Europe, I would encourage you to buy a copy of Rick Steves' Europe Through the Backdoor book (or check a copy out of your local library). It's a book that helps with travel skills in Europe. I read it before my first trip to Europe in 2014, and it was immensely helpful.

I agree with the recommendation above to get as good seats for the opera as you can. I had great seats and had zero regret regarding the splurge to get them.

I personally would consider a Munich--Salzburg--Vienna itinerary.