We spent the majority of our trip to Iceland in Reykjavik, the capital city of about 120,000 people (the whole country only has about 320,000). Reykjavik is a very nice city. It is very walkable, and has a number of different things to do. Some of the highlights included the Culture House, which houses many of the original Old Icelandic manuscripts documenting all the names of the settlers of Iceland, as well as many of the sagas, such as the discovery of Greenland and North America. We also went to the Settlement Museum, which is relatively new (2001), which has an excavation of a Viking settlement from 871 +/- 2 years.
One of the really cool things about Reykjavik is all the public art they have. One trend we noticed in several places is some shimmering pieces of art, which, upon closer inspection we noticed are composed of small metal discs which all move independently of one another. I took a little video to illustrate it.