Several options are for travels between Akureyri and Reykjavík and other places within North Iceland. Flights, buses, ferries and taxis to mention the most common. Within Akureyri the city buses are for free.
Regarding travel to the islands Hrísey and Grímsey information on ferries and buses can be found on the timetables according to the season:
Summer
Winter
as well as how to get from Akureyri to Dalvík.
For more information on domestic travel visit www.visitakureyri.is/en