The obvious day trip from Akureyri is Lake Mývatn, 100 km east along the Ring Road. Mývatn is one of the most geothermally active areas in Iceland: the Hverir sulphur fields smell strongly of rotten eggs and look like the surface of another planet; the Dimmuborgir lava formations are a maze of black rock columns that local folklore associates with trolls; and the Mývatn Nature Baths offer a less crowded alternative to the Blue Lagoon, soaking in geothermal water with views of the lake. Dettifoss, Europe's most powerful waterfall, is 60 km east of Mývatn along the paved road.
Closer to town, the Goðafoss waterfall is 50 km east of Akureyri and easily combined with Mývatn. The falls themselves are not as dramatic as Dettifoss, but the history is extraordinary: it was here in the year 1000 that Iceland's law-speaker Þorgeirr Ljósvetningagoði threw his statues of the Norse gods into the water after deciding Iceland should adopt Christianity.