Islands Akureyjar are a group of 30 islands and vegetated islets, which were considered to offer the best habitation and advantages of the Islands of the Breidafiord Bay.  The home island is almost in the centre and therefore its boat landings are sheltered.  During low tide, quite a few islands and islets are accessible on foot.  The distance to the mainland is rather short in both directions.  Most of the islands are vegetated and well suited for eider colonies and other bird species.

Island Baejarey, situated in the northern centre of the island group, is the largest.  Attached to it is Island Akurey, where there are traces of ancient grain crops cultivation.  The island group is mentioned in several places in the Sturlunga Saga, but there are no clear indications of its permanent occupancy at that time.  It was, however, considered advantageous for the owners at farm Stadarholl.  In 1704, seventeen people were registered there.  They owned 11 heads of cattle and 33 sheep.  Later in the century, it was abandoned, but occupied again in 1804.  The water supplies were unreliable until one of the farmers deepened the well, and since then there has been no lack of freshwater.

Several workers, who shepharded about 50 sheep during winter, inhabited one of the islands, Lyngey, for a while.  For that purpose the farmer built accommodations and a sheep shed for about 50 sheep on the island.  The total number of sheep on the islands remained between 150 and 200 for years at that time.  The last family to live on the home island left it in 1954 and since then some of the advantages of the islands have been exploited up to this date.

According to popular belief, elves occupied Island Hofn.  They were both friendly and helpful in times of need.  They burned fires to help the humans sailing back from the mainland in bad weather conditions find their way.  Other elves probably occupied a mound on Island Baejarey.