There are a few threads on Reykjavik that might help...but you need to spell it correctly :)
I like a tiny place on the harbor near the Icelandair hotel. The sign just says "lobster soup". Very casual, very affordable. The soup is sublime.
Try some ice cream and a hot dog from a stand in a town square. Tasty and cheap!
I also enjoy an Indian place called Scheherazade. A bit pricey but really delicious.
If you're coming from the US, expect to spend more on food than you think you will. Enjoy!