Happy Wanderer,
there are 3 opera-houses and a lot of venues for classical music in Berlin, so you will have a good choice there. Your hotel will probably have enough information on whats going on when you are here (and they will be able to get the tickets for you too). The "Konzerthaus am Gendarmenmarkt" is a beautiful place and often has very good concerts.

As for folk - you might find something in more concert-like venues as well as smaller pubs that are less noisy (the "Union Jack" that Wolfgang mentioned is a very small one but has music only occasionally. Another good one with regular music would be the "Celtic Cottage" in Steglitz - www.celtic-cottage.de On the first Friday evening of the month the "Cafe Central" in Handjerystrasse hosts a beginner friendly session that I usually attend).
If I knew the exact dates of your visit I could look up what is recommendable - why don`t you join up the mudcat so I could send you a personal message?

Apart from the music the National Gallery on the Museumsinsel is very nice and the Gemäldegalerie at the Kulturforum hosts a very good exhibition about Rembrandt - lots of important works. It ends at November 5th, so maybe you have a chance to see it.

I also second Tootlers recommendation of taking a boat trip. Make sure to take the long one that does a circle through Landwehrkanal instead of the shorter one that takes the same way back and only covers the city center.

Feel free to ask me if you are interested in specific things!

Best
Ernest