One local speciality is Kefalonian meat pie, available in quite a few restaurants. It's a hearty farmhouse thing rather than haute cuisine. Getting a really good example is not easy, however - the Captain's Table in Argostoli is perhaps your best bet for this local dish. Food in most establishments is okay rather than spectacular. Menus tend to be the same in most places; its worth tapping into local knowledge about where to eat.
If you're in Argostoli, visit the big bakery on the main street opposite the harbour and buy the little round cheese pies - they're fantastic
There is a lovely cafe/restaurant at the entrance to the Venetian fortress in Kastro, shaded by trees, with very friendly owners - a Greek man married to an English woman Nicki. The homemade cakes here are delicious.
Moreover, there is a lovely tavern Dionysos in Poros, which a spectacular view to the island of Ithaca and the marina. There you may find one of the most mouth-watering meat pies kreatopita in the island, as it is prepared according to a traditional Kefallonian recipe contains up to tree different types of meat. Additionally, slightly exotic scenes in Dionysos are the squids that slowly dry while hanging under the sun, waiting to be fried. Nonetheless, the specialty of the restaurant is mousakas, a small bite of which leaves a mouthful of flavours.