In the old town of Akureyri one can find plenty of nice photo spots - on our FB page Visit Akureyri you find plenty of photos taken in that area that can help you see what is in that area.
We can e.g. point out the main street "Aðalstræti", the Akureyri Museum, the church close by the Museum and the Nonni house. Also the area by the Industry Museum is worth a visit - just 10 minutes more walk to the south from the Akureyri Museum (behind the skating rink).
By the Industry Museum you find a old park and the Motorbike Museum and jet 10 more minutes walk south from this area, in the Airport Area, you find the Aviation Museum.