This is a great way to get to see the city with excellent background stories by a local guide. The Reykjavik Food Walk is one of the highest rated tours of Iceland. It offers great food in a great selection of restaurants, complete with explanations on ingredients and history of the dishes. Overall a great experience and ambiance.
Note: the meeting location for The Reykjavik Food Walk is at Harpa Concert Hall. Look for the guide with the bright blue backpack.