The simplest way to visit our island is by direct flight to the international airport of Argostoli (EFL). Airlines from many European countries offer direct charter-flights to Kefalonia.
If such a flight is not provided in your country, you can fly via Athens and connected flight to Kefalonia or fly to neighbour destinations such as Araxos (Patras), Aktion (Preveza) or Zakynthos and then continue by rented car and Greek ferries.
Look here for flights Athens – Kefalonia
Aegean Airlines
Sky Express