You might better ask how you can avoid doing so. There are a lot of classical music concerts in Vienna. A lot.
The city has a musical heritage like no other, one that continues today. So where can you find the right date, venue and ticket?
Strauss & Mozart concerts
Several orchestras and venues specialise in providing an evenings-worth of classical entertainment for tourists and other visitors, mostly featuring the more well-known works of Mozart and Strauss. These include:
Putting on a little music at home means something quite different when you’re an Emperor. For Joseph II, for example, it meant inviting Mozart to perform a new opera in the Orangery of Schönbrunn Palace. Daily concerts continue the palace music tradition today. (Visitor and concert tickets info)
The Kursalon hosted waltzes back when they were the new music craze sweeping the
nation empire. It revisits that history with a daily concert. Take the opportunity to grab a photo with the golden statue of Strauss just outside. (Visitor and concert tickets info)
Vienna Mozart Orchestra
The orchestra, singers and soloists perform in period costume at different historical venues, including the Musikverein, Konzerthaus, and Staatsoper. (Visitor and concert tickets info)
Traditional concert houses
If you’re looking for the more “traditional” experience in one of the active concert halls with changing repertoires, then Vienna offers some of the planet’s greatest venues with world-class performers from around the globe.
Possibly (probably?) the best classical music venue in the world. Names like Brahms, Mahler, Schoenberg, Strauss, and many more are intimately associated with this 1870 building that also provides a home for the famous Wiener Philharmoniker orchestra. (Visitor and concert tickets info)
Another internationally-recognised top venue for classical concerts, the Konzerthaus repertoire also features jazz, world music and various other genres of musical endeavour. The 1913 building has four concert halls, hosting hundreds of events from September to June. (Visitor and concert tickets info)
…and don’t forget the opera houses.
Other concert venues
If the above isn’t enough, the official city tourist site has events listings.
Look for the “events” icon, which should bring up a search interface. Put in your dates and hit “search” (or “suchen” in German). You can also narrow the search by category. I did a search for concerts for a single, random Monday in September and got 20 different options.
If you’re visiting churches, look out for recitals and similar there. Vivaldi’s Four Seasons is playing at Stephansdom cathedral, for example, as I write this article, and many churches also have advent concerts during the Christmas period.
The last couple of times I’ve been on the Graben, the pedestrianised street at the heart of the city, I’ve encountered classical street performers, including a small string ensemble and an opera singer accompanied by the flute. Vienna in a nutshell, really.
The Rathaus film festival typically runs from the end of June to the start of September, displaying “films” on a giant screen in front of city hall. The square not taken up by seating is turned over to a gastronomic journey through Austrian and international cuisine.
What’s this got to do with anything?
Well, the reason I say “film” is because most of the screened entertainment is actually music and a large chunk of that is classical music. In 2018, the programme included Mozart’s Requiem, the Nutcracker, Carmen, and various Bernstein-directed performances of works by Beethoven.