Question for our German and Swiss fabo family

I will be going to Vienna Austria on the 12th of January for 7 days on a business trip. What should I see while I am there? Anything to avoid? By the way, I am a huge WWII buff an love history. I am also laid over in Copenhagen Denmark for one day. I plan to buy my wife some swarovski chrystal while I am there, but that is about it while in Vienna.

Help me out ULI!!!