In some parts of Greece there are very good weekly street markets, λαïκή ('likey'), e.g. on the mainland at Ermioni, near Hydra. There are no weekly general markets on Kefalonia but there is a large permanent (predominantly) fruit & veg market along the seafront in Argostoli and, behind the bus station, small market stalls selling their own locally grown seasonal produce.
At the festivals of Agios Gerasimos you’ll find a multitude of market stalls selling a very wide variety of items, from carpets to pets to traditional wooden wine barrels (plus the usual tat). There’s also a (much smaller) market at the Markopoulo festival.