If you're looking for outdoor adventure, make a day trip to Hlidarfjall Akureyri. No easy stroll around the block, this hike is great for some mid-vacation exercise.
When you've finished up at this steep landmass in Akureyri, why not make your way to Hof - Cultural Center and Conference Hall, Akureyri Church, and Akureyri Botanical Garden? They're not very far from Hlidarfjall Akureyri and also popular with tourists.