A bed in a four-person dorm costs ISK3,400 (£17), while a private double is ISK11,700 (£58). Take a view The harbourside has been transformed by Harpa (8), a vast concert hall conceived during Iceland's boom years.
Where the harbour wall turns north, the Maritime Museum (9) tells the story of life on Europe's raw edge (00 3; reykjavikcitymuseum.is; 10am to 5pm daily; ISK1,400/£7).
The historic core of the capital (known as 101, after the local postcode) lies between the harbour and an inland lake, Tjornin.
The city's helpful tourist office (3) is at Adalstraeti 2 (00 3; visitreykjavik.is).
The Marina Hotel (5) at Myrargata 2 (00 3; icehotels.is) is a 21st-century place to stay, housed in a 20th-century paint factory next to the harbour's dry dock.
The public areas on the ground floor are whimsical, while the comfortable rooms come equipped with instructions for tying knots or learning Icelandic phrases.