Hallgrimskirkja Church towers over the city. Hop on the elevator to rise 75 meters into the spire, where you'll enjoy panoramic views. In the surprisingly understated interior, you'll find the vast 5,275-pipe organ, upon which an organist performs near-daily concerts.
Grab the free shuttle bus every half hour from Harpa Music Hall to the Perlan Dome, which reveals the wonders of Iceland through exhibitions that include a man-made ice cave, a planetarium and an interactive glacier show. The observation deck puts your attention on the natural wonders of Iceland, including mountains, geothermal areas, the ocean and a glacier.