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.