I recently went to National Gallery of Iceland to see Hrafnhildur Arnardóttir aka. Shoplifter exhibition. Hrafnhildur has for the last 15 years been working with hair in her arts. She says that "Her art addresses the history of our obsession with hair and how it is an ongoing manifestation of creativity in contemporary culture, tackling notions that border on obsession or fetish." She is playing with colors and texture, that gives the audience a playful environment.
The National Gallery of Iceland is a small gallery but has a good collection of Icelandic art, that includes some of my all time favorites. You can also find a cute small coffee house in there and a small shop with all kinds of designs. The entrance fee is 1500 isl. kr. and with the ticket you can visit two other galleries, so I would say it's worth it!
National Gallery of Iceland - Fríkirkjuvegi 7, 101 Rvk.