A walking tour with CityWalk Iceland. It gives you a detailed background of the history of Iceland, an incredible understanding of Viking pride and a blueprint of where to go and find information in Iceland. At the end of the tour, you'll get an email with things to do within the city and also a link to join their weekend pub-crawl. (great night out)
The tour terminates at Reykjavik City hall. There you can find information on most things to do in Iceland. There is also a map of Iceland on the inside of City hall.
Feed the birds. Outside of city hall is the great pond where Icelanders come to feed the birds on Saturdays. It's a tradition, plus you get to learn a lot about the different types of birds in the pond.
On the other side of the pond is Skáldabekkur (TheLiterary Retreat) The statue is quite cool. It’s a great place to come and relax and just take in the atmosphere of the city.
Spend an afternoon at the Harpa Concert Hall. If you’re lucky enough to attend a concert here, please do so. The building is absolutely magnificent. From the inside, you can find amazing views of Reykjavik harbor. Climb the stairs and the views just get better. At nights, the glass on the outside of the building changes colors. It is truly amazing.
The Solfar Sun Voyager is a steel structure that resembles a Viking ship but offers a treat for the eyes and a great way to see views of Mount Esja on the other side of the harbor.
Towering above the city is its largest church Hallgrìmskirkja. The tower within the church is accessible for ISK 900. Do it, you won't regret it.