Akureyri is the largest town outside of the capital area in Iceland with a population of 15,000. It is located on Eyjafjordur Fjord. It’s mostly an industrial town with shipping and dairy industries, and home of Akureyri University. Akureyri also is the site of the second oldest gymnasium (high school/college) in Iceland.
Sights include the folklore museum and the botanical gardens. A trip to nearby Lake Myvatn should also be on your list.
Referred to by Icelanders as the Capital of the North, Akureyri has a surprisingly active cultural life for such a small town. A number of art galleries operate year round, and a professional theater company operates during the winter. There is plenty of nightlife, with places such as the relatively large dance hall Sjallinn, where Icelandic bands play most weekends, Kaffi Akureyri which is a bar with a 25-35 year old crowd and a dance floor, and quiet coffee houses Kaffi Bar, Kaffi Karlna and Bla Kannan.