This blog post discusses the variety (limited!) for grocery shopping in Reykjavik:
https://iheartreykjavik.net/2013/07/...ng-in-iceland/
In another post, the author suggests the IKEA cafeteria as an inexpensive way to eat in the city. As "Out of my Element" mentioned, you can bring in your own food to supplement groceries. Not just dried nuts/fruits--you can bring in six pounds of food, legally. I'll have a bunch of Clif bars, myself.
Have a great trip!