Many events/performances/concerts take place in the "Neue Welt", a concert hall from the Art Nouveau era. It's located quite a distance north of the old town but trams #4 and 7 stop right in front of it and run till after midnight. Tram and bus are usually included in the ticket prices.
I was fortunate enough to attend a symphonic concert on occasion of Gustav Mahler's anniversary - the symphonic orchestra Zwickau-Plauen performed some of his songs, soloist was Shin Taniguchi, an excellent baritone I had heard live in Görlitz before. The main event of the concert was Mahler's 9th symphony, though, a really tough to play piece. They did very well, much better than I had expected. Not exactly in the league of the top orchestras, but not far behind. The ticket was only 18 Euro (excellent seat) - a steal.
The concert hall has a capacity of about 1,000 people. They also have pop, rock, jazz and other live music there as well as galas, shows and musicals. See their website for schedules.
Dress Code: For concerts and galas dress up a bit. Coat and tie not required but recommended. Otherwise casual - jeans are fine.
When looking for an evening activity don't neglect the theatre. Zwickau's theatre has its home in the Gewandhaus, the former guild house of the clothiers. From 1823 on it was used as theatre, after more construction works it was reopened 13 Nov 1855 with the opera "Die weiße Dame" by Boieldieu. From the year 2000 on Zwickau's Theater has a co-operation with the theatre in nearby Plauen to save money. Result is an improvement in quality. They perform opera, operetta, musical, plays, ballet, even have a puppet theatre.
When I was in Zwickau I attended a performance of Brecht/Weill's "Dreigroschenoper" (Threepenny opera) which was very well done. I was actually amazed at the quality of the singing as the soloists were actors in first place. The production was very good, too. Not overly modern, but not kitschy/old-fashioned either. What surprised me was the number of young folks - about half or two third of the audience were under 25, I'd say. The ambience in general was pleasant as well. People gathered in front of the theatre or in the lobby upstairs and had a drink, chatted, before the performance and during intermission. Prices for drinks are very reasonable, btw.
Tickets are available online or from the box office. Prices are dirt cheap. A good deal is that tram/bus are included before and after the performance (I only had a three minutes walk to the theatre, a shame. :-))
Box office opening hours:
Tue/Thu/Fri 10-18 h
Wed 10-15 h
Sat 10-13 h
Dress Code: Mostly casual, but I saw guys in jacket/ties and ladies in finer robes as well. I dressed up a bit and didn't earn stares.
In one of the Priesterhäuser townhouses plus some modern buildings in the back is a microbrewery plus beer pub/garden. Entrance is from both sides, Peter-Breuer-Straße (which is called the "Pub mile" - Kneipenmeile) and the Domhof square. Since 2001 they brew their own beer. Really tasty. I had one Pilsener and one Wheat beer (which is my favourite).
It's a great place for hanging out with friends (or colleagues on a business trip). Have a table either in one of the charming rooms with old wooden ceilings or outdoor, either in the beer garden or in the courtyard. The view of the lit up Dom St. Mary adds to the romantic ambience on mild summer nights.
I was told the food is pretty good also. No personal experience, though.
Dress Code: Casual. Dress as you please. Frequented by students but also business folks.