Things to do
10-

Grótta Lighthouse
The darkest sky within walking distance of the capital, which is why aurora watchers head west to the shore rather than out of town.
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Hallgrímskirkja
A lift runs to a viewing deck near the top, and the coloured grid of Reykjavík's roofs only makes sense from up there.
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Harpa Concert Hall
It was the only construction site left standing in Iceland after the 2008 crash, finished by the state as a point of principle, and the foyer costs nothing to walk into.
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National Museum of Iceland
The Valþjófsstaður door, a carved medieval church door showing a knight, a dragon and the lion he frees, justifies the visit on its own.
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The Sun Voyager
It was meant to face west into the setting sun; a change to the road plan turned it north instead, and the sculptor let it stand.
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Laugavegur
The name carries the city's whole history in one word, from laundry route to its busiest street, and it climbs straight to Hallgrímskirkja.
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Perlan
A working piece of the city's hot water plumbing that happens to carry a free 360 degree deck, so the view costs nothing even when the exhibits do not.
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The Settlement Exhibition
The oldest known building in Reykjavík is still sitting in its own hole in the ground, with the modern street built over the top of it.
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Tjörnin
It freezes hard enough for skating most winters, apart from the corner kept open with warm water, where every duck in the city then crowds in.
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Viðey
Serra set nine pairs of basalt columns around the shoreline so that walking between them measures the island, and the Peace Tower throws a column of light from 9 October to 8 December each year.