Akureyri is what Icelanders mean when they say the capital of the north, and the title is only half a joke. About 20,000 people live here, at the inland end of Eyjafjörður, one of the longest fjords in the country. Permanent settlement began in 1778, the king gave it a town charter in 1786, took it away in 1836 and gave it back in 1862. It has a church on a hill, one of the northernmost botanical gardens in the world, traffic lights shaped like red hearts and a pool where half the town meets in the evening.
The town is the smaller part of the reason to come. From here, Goðafoss is 34 km away, the Mývatn lava fields about 80 km and the whale-watching harbor of Húsavík 76 km, all close enough for a round trip in a day. That's why three days is the right length: one for the town, which doesn't need more, and two out-and-back days. A fourth day is an easy add, and the If you have more time section lists what goes in it.
Day one stays in town, day two is Goðafoss and Mývatn, day three is Húsavík. Any start day works: in winter the Akureyri museums are open daily from 13:00 to 16:00 and the Húsavík Whale Museum from 10:00 to 16:00, so only the short hours matter. This guide covers the north of Iceland. Winter changes this plan a lot, and every day says how.