We really didn't spend a huge amount of time in Reykjavik, and honestly, I don't think you should either. There's so much more to see in the countryside that will leave you speechless that you don't really need to spend more than half a day in Reykjavik. Nevertheless, we used Iceland's capital as our home base for a few of the days during our stay there. Here are a couple of my tips for the city:

Coffee

Reykjavik Roasters
Stofans

Food

Grillmarkadurinn
Laundromat

See

Hallgrimskirkja (make sure you take the elevator up the tower for the best views of Reykjavik)
The Icelandic Opera
 

Hallgrimskirkja