1. The Sun Voyager: Located on Reykjavik's waterfront, this iconic sculpture represents a dreamboat and a symbol of hope and freedom.

2. Harpa Concert Hall: Marvel at the unique glass façade of this modern concert hall and enjoy free exhibitions, events, and occasional concerts.

3. Hallgrimskirkja: Visit the famous church, take the elevator to the top of the tower, and enjoy panoramic views of Reykjavik.

4. Reykjavik City Hall: Explore the exhibitions and galleries showcasing the history and culture of Iceland, located overlooking the picturesque Lake Tjörnin.

5. National Museum of Iceland: Immerse yourself in Icelandic history and culture through the engaging displays and exhibitions in this national museum.

6. The Icelandic Phallological Museum: Discover a curious collection of more than 280 specimens illustrating the male genitalia of various animals.

7. Reykjavik Art Museum: Visit the Hafnarhús, Kjarvalsstaðir, and Ásmundur Sveinsson Sculpture Museum, as they often offer free entry to certain exhibitions or parts of their collections.

8. Reykjavik Street Art: Explore the city's vibrant street art scene by taking a walk through the downtown area and discovering numerous colorful murals.

9. Tjörnin (The Pond): Take a leisurely stroll around this picturesque lake, home to various bird species and surrounded by beautiful parkland.

10. Austurvöllur Square: Spend time in the lively square, considered the heart of Reykjavik, and soak up the atmosphere of Icelandic street life.