The dramatic lava cave at Lofthellir is a stunning destination, with magnificent natural ice sculptures (ice trolls?) dominating the interior.
Although it's one of Mývatn’s highlights, the cave is on private property and can only be accessed on a half-day tour run by Saga Travel . The tour involves a 45-minute 4WD journey and a 20-minute walk across a lava field to reach the cave itself, and then special equipment (headlamps, studded boots etc) and some wriggling through tight spaces. Dress warmly.
The tour costs Ikr26,500/19,500 from Akureyri/Reykjahlíð. Note, too, that Saga Travel also offers this tour in winter, which involves snow-driving and then snowshoeing to access the cave (Ikr34,500/27,500 from Akureyri/Reykjahlíð).