You'll hear about the golden circle—a three-stop tour of some of the most wonderful natural and historical things you'll ever see—and you'll also be told repeatedly that it's not a circle and it's not golden either. A half-day trip that takes you to geysers, the site of the old Icelandic parliament and location of the tectonic continent shift, and a stunning waterfall, the outing is both memorable and fun—but it's also tourist heavy and organised so that there's little deviation.

Hire a car instead and splice some side-bar diversions into the day—like a visit to the picturesque Hveragerði, 45 km to the east of Reykjavík. Around 2,000 people live here and the town is a geothermal paradise. Hike the three-hours to Reykjadalur, a valley where you can bathe in the stream.

For a more substantial trip, instead consider driving around the Snæfellsnes peninsula, 150 km to the north of the city. Often called “Iceland in miniature”, the peninsula features almost all of the features that dominate Icelandic nature in one spot, including a sub-glacial volcano, ancient lava fields, hot springs, rolling hills, wind-blasted beaches, fantastic rock formations, majestic waterfalls, lonely lighthouses, and small settlements dotted along the coast. Furthermore, you can be there and back again in twelve hours if you have your own car.