Vivaldi concert or opera

https://www.wiener-staatsoper.at/en/

This is the official opera site. See what's available when you're there. I greatly enjoyed Marriage of Figaro in September.

Because if a concert is for tourists, it is not necessarily touristy, i.e., low quality. Vienna is the city of classical music and houses an enormous number of excellent musicians, switching between different orchestras, playing at renowned locations.

There are concerts of mediocre quality, though, mostly tickets for those are sold on the street. Refrain buying tickets from inofficial channels, especially avoid scalpers trying to sell you tickets for the Staatsoper. It will be a rip-off.

For beginners regarding classical music I can recommend the following.

The already mentioned Four Seasons by Vivaldi, played on historic instruments of that time. The auditorium, the church, is flat, so the view from rows further away from the stage is not too good. You can buy the tickets from several online sources, but I recommend this one, because it is the only one allowing you to select your seats from the floor plan:
https://www.concert-vienna.info/

Very popular are concerts of music composed by Mozart, played by musicians donned according to that time. I can recommend this one, being performed in the famous Golden Hall, the concert auditorium said to have the best acoustics in the world:
https://musikverein.at/konzert/wiener-mozart-orchester-00060874/

Opera performances at the Staatsoper are already sold out for your time frame, and maybe not the best choice for beginners. An alternative would be the Magic Flute by Mozart, performed at the Volksoper. It is a rather modern production, singing is in German, but there are English surtitles:
https://www.volksoper.at/production/die-zauberflote-2025.1014664295.en.html

Please note that October 26 is Austria's national holiday, i.e., all shops are closed as well as a significant number of restaurants.

I personally love Vivaldi, so I'd go for that.

Off topic: I went to a Chopin concert in Gdansk. It was touristy, but it was also nice. One artist played the piano, the other plaid the violin. Me? I cannot play anything to save my life, so I appreciated the concert.

I'd say, depends on the price. What are you comfortable paying?

Vienna was home to many great composers, Mozart, Hayden, Beethoven, Brahms, Schubert and Johann Strauss to name just a few. As a beginner in classical music and being in Vienna, consider a concert of music by Johann Strauss, aka the Waltz king. He also composed some light-hearted operettas, the best known being Die Fledermaus. Another good choice would be music by Mozart. Go to the Wien.info web site, you will find listings of concerts taking place in Vienna, I am sure you will find something that appeals.

If I were you, I would consider whch ever performance you can still get tickets for.

As for "tourist" or not. You are a tourist with very little ability to tell great music from average music so dont sweat it. For you its a presentation of the local cultural arts.

Enjoy.

Just to add to all the great advice about composers above, I would listen to some opera and see if you like it! I can only handle 2 hours of Puccini, but that's about my max, and almost nothing in German. But that's just me! I think Vivaldi Four Seasons in Vienna would be amazing, I love music in European churches, I wouldn't worry about it being touristy either. Enjoy your time in Vienna!

Well if you are going to get serious about it. You need to do these two courses.

First this: https://shop.thegreatcourses.com/how-to-listen-to-and-understand-great-music-3rd-edition

Then this: https://www.thegreatcoursesjourneys.com/greatmusicmasters2

Thank you all for your great answers, input and links, i appreciate =)
We are for sure going to do the Vivaldi Four Seasons and I am now looking for the Mozart at the Musikverein as a second one.
Merci

We were in Vienna mid-September, and we ended up attending both, but I had booked our opera tickets several months in advance. I wanted to attend the Vivaldi concert because the Four Seasons is nostalgic for me. When my kids were growing up, we listened to the children's CD of Vivaldi's Ring of Mystery so many times! Also, the concert gave us a chance to see the beautiful Karlskirche. I was also intrigued (and saddened) by the story of how Vivaldi ended up being buried in Vienna. A forum member here alerted me to look for the plaque on the building next to Karlskirche that commemorates his burial. As for the performance, we enjoyed it very much. The lead violinist is perhaps a bit theatrical in his performance, and they do sell their CDs afterwards, but neither of these things bothered us.
We saw the Marriage of Figaro at the opera house and it was wonderful! If you can get tickets to an opera, you might find it helpful that each seat has a screen where you can see subtitles in your chosen language. We dressed up a bit and also reserved refreshments at intermission. This evening was an elegant splurge for us.