Find your guide in front of Hallgrímskirkja Church by the statue of Leifur Eiríksson. This is on a hill and the highest ground in Reykjavík, from which you can get an overview of the area. From that point, you will walk downhill.
The guide will take you through various streets of Reykjavík, passing by important buildings of great architecture, and will detail their history as you walk by. You’ll get a great introduction to Iceland's history and culture. See the Harpa Concert Hall, beautiful on the inside, which also serves well as a warm stop on cold days which are frequent in Iceland.
Continue the walk along the oceanfront before eventually moving to the oldest part where the parliament and city hall is located.