To avoid tourist traps I would definitely go for Musikverein or the State Opera. I can strongly recommend planning a little beforehand and book tickets in time rather than fall for one of the Mozart dressed vendors on the streets. The many touristy concerts tend to promise a lot but the quality of music just doesn‘t justify the ticket prices and they are packed with tourists only.
Jeunesse (http://www.jeunesse.at/) concerts usually offer good value (especially it you are < 26 years old)
For classical music you cannot really go wrong with the two main concert halls (the Musikverein and the Konzerthaus) and the two main opera houses (the State Opera and the Volksoper). The concert halls also offer good non-classical music — the Konzerthaus in particular offers great Jazz and World Music performances.
Tickets are actually usually pretty affordable, especially if don’t care too much about the view. The acoustics are pretty good in all the venues (the “Große Musikvereinssaal” in particular is famous for its acoustics).
If you are on a budget there is one important thing to know about the Viennese music halls and opera houses: they all have “Stehplätze” (standing places) for about 5-10 Euro (I’m not sure about the Konzerthaus, but I checked the others). They are usually located in the very back, but you can still hear the music very well there. The State Opera has standing places on several levels and you might get a better view from the ones higher up, especially if you are late and the good ones downstairs are already taken. After the intermission you might even be able to get a seat.
I’ve been to two concerts in Musikverein, and while they are no Opera, the experience is well worth it. Prices are reasonable for that sort of thing (in the range of 30 to 70 EUR, if memory serves), and the acoustics in the Great Hall (Großer Musikvereinssaal) are great, apart from the lavish gilded decoration. Dress code is somewhat relaxed compared to high-end classical performances (suits and evening dresses certainly not required, though of course welcome).
Tickets are typically available online, or even from those Mozart-dressed guys you’ve seen in front of St. Stephen’s Cathedral. AFAIR, they charge face value for the tickets, but of course it’s better to book them yourself online and collect before the concert.
When we were in Vienna last year we went to a concert at the Wiener Konzerthaus which we enjoyed. Their programme is quite extensive and there are smaller and larger halls in the building so you could see a small recital or an orchestra. It’s just outside the city centre but easy enough to get to and seemed to be well frequented by locals rather than tourists.
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