On a Thursday night, my friend and I were walking towards the Old Harbor and noticed a lot of people going into this building. We followed suit and ended up buying 2 cheap tickets to the symphony. It was a delight; a great side trip. The seating was wonderful and the building is spectacular inside and out. I recommend planning ahead and catching a performance, even if it is Icelandic.
You can also get a tour of the building. I'm not sure if there is a fee for the tour, but there is a fee for the performances.
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