Reykjavik for The Curious Wanderers: a Friday-to-Monday weekend

Start with a free walk to the steel ship sculpture facing Esja, the postcard everyone has seen; the light turns pink on the mountain at dusk.

A year-round northern lights exhibition with time-lapse films and a short photography lesson, which helps since the real thing is a lottery.

Traditional Icelandic food opposite the church: rye bread with smoked trout, lamb soup and rye-bread ice cream, which tastes better than it sounds.

Mud pots and sulphur-yellow vents on a boardwalk 40 minutes south of town; stay on the planks and expect the smell to follow you into the car.

A small footbridge across a rift 15 metres wide between the North American and Eurasian plates; free, windy and quiet. Check the Reykjanes road status before you set out.

A museum built around the replica Viking ship Íslendingur, which sailed to New York in 2000; it shows the voyage, and the sagas, indoors.

Back in town for charcoal-grilled Icelandic lamb and langoustine in a room of basalt and wood, where the food is the point.

A five-minute ferry to a car-free island with Richard Serra's basalt Áfangar and a ruined village; sails daily in summer and at weekends in winter.

A glass dome on a hill holding a glacier exhibition, a man-made ice cave and a planetarium; the viewing deck is free with a ticket.

Burgers, ribs and a local craft beer list in a loud room, good value by Reykjavik standards, and fine for people who walked all day.

Pre-book a morning slot for the milk-blue silica water on the way to Keflavík airport. Eruptions near Grindavík have closed it before, so check its status the day before.

Iceland's largest mud-spring area at the tip of Reykjanes, steaming and hissing beside a lighthouse; keep to the boardwalk, since the ground is hot.

Fish soup and the catch of the day in a harbour restaurant before the short drive to the airport.