Akureyri, the second biggest town in Iceland, has so many things to offer. If you are spending time in this charming town, this article by Dísa—who lived in Akureyri for several months—is a fantastic read.
Reykjavik Classics is a concert series featuring live classical performances at Harpa two times a day for the rest of the summer. Each concert is only 30 minutes long—a perfect addition to the mandatory visit to Harpa.
Guided tours are nice but saving money by doing stuff on your own is even better. There are in fact a lot of activities you can do for free in Iceland, such as hiking, sight-seeing and bathing in natural pools.