Two ugly concrete buildings dominate the beautiful Tjornin Lake in Reykjavik's downtown. You might think they're some warehouses or car repair places, but no - this is the capital's City Hall, probably the ugliest I saw worldwide. The better part is you can enter it for free via small pedestrian bridge. Very clean restrooms to use and free wifi. The highlight and the only reason for entering (besides the restrooms) is a terrific huge 3D map of Iceland displayed in the lobby.

The Reykjavik City Hall is a modern structure built on a pond, with walkways over the water and interesting architecture. There are nice views of the pond, and some interesting statues and pieces of art. But the most surprising feature is the giant relief map in the lobby of the whole of Iceland. It is worth a quick look. Speaking of relief, there are also public washrooms in the building, free of charge.

A somewhat sixties structure, lots of concrete and boxy. The setting is quite good, next to the water the columns along the front male a picture. There is a large relief map/structure in the basement you can visit, worth the effort.