If you are looking for big game fishing than you are in the wrong part of the World. The Mediterranean sea has been over fished for far too long to hope for any really large fish.
But going around Corfu you will not help but notice a lot of people with rods fishing day after day and taking home a reasonable catch. If you set your sights for small, but very tasty fish you will not be disappointed.
Corfu is one of the better islands in Greece regarding fishing, in fact up until recently the village of Benitses was considered to have the best fish anywhere in Greece.
One of the reason Corfu has more fish than other islands are the three large lagoons which act as breeding grounds and supply a significant percentage of the fish in the markets so the waters around the island are not fished to death.
With a little study and modest expectation fishing can be very enjoyable for all the family as it is very accessible with hundreds of rocky points and piers to throw a line, sometimes with surprisingly good results.
Serious anglers can hire small boats and try for larger fish in deep waters over the many reefs and while decent catches are not uncommon, patients will be a necessity rather than a virtue.