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- pay to get up Hallgrímskirkja and enjoy the view
- eat Tromp
- visit Norræna húsið, where they have the biggest collection of Nordic books and movies
- go drink tea and eat cake (and play board games) at Café Babalú
- go swim, f.ex. in Laugardalslaug
- walk around (for hours) and enjoy all the pretty graffiti walls
- see a band play, preferably at Airwaves and/or in Harpa. or just go to 12 Tónar.