The western part of South Iceland is in many ways Iceland's agricultural heartland, and hosts many traditional Icelandic farms with sheep, cattle, horses, and other animals. It's one of the main dairy producing regions of the country, producing most of the milk consumed in the capital region. Further east, aquaculture and fresh-water fishing plays an important role. Arctic char from Kirkjubæjarklaustur is known in Iceland as a delicacy. Also worth mentioning is the farm Þorvaldseyri (http://www.thorvaldseyri.is/en), the only place where wheat is grown in Iceland. You can buy it straight from the farmer.
Awareness of the value of local produce is increasing, and farmers markets are becoming ever more common in South Iceland. You should also ask in restaurants whether they have some local specialties, chances are that they do.
Famous for lobster and lobster soup.