There are a few options:
1.Take the M3 train from Athens Airport towards NIKAIA and get off at Monastiraki.
Google Maps Directions
2. Get a taxi using Uber. Uber operates in Athens but you basically book a yellow local taxi with a meter. Always prefer Uber rather than getting a taxi at the street. Uber drivers are always nicer and you don't have to worry about paying with cash.
3. Arrange a pickup using WelcomePickups. The price currently is €40. We've used them before and were really nice.
Welcome Pickups
To go to Patras port we will arrange a private transfer.
The option we are looking at now is a 10 people carrier Mercedes Benz Sprinter and they have quoted us for €520. We will also arrange this.
To be able to be at the port 2 hours before we will need to leave fresh hotel at 7:40 am
From Patras, we get the boat to Ithaca. It costs €15 and it takes 4 hours.
No need to worry about booking this one, we will book for everybody nearer the time when tickets are available.
Ithaca is a small island but we still need to hire a car to be able to go the town for supplies and explore a little bit. We are in touch a couple rental companies there to get a quote. We are thinking two cars and the total cost would be approximately be €600.
To leave Ithaca on the 15th of July, we will get a sea taxi over to the capital of Kefalonia, Argostoli, which is a short taxi ride to the airport.
We are going to get in a touch with Sea Taxi Odysseas to get a quote and book this in advance.
From Kefalonia airport you can then book an evening direct flight to Athens or other European cities such as London.
Please don't book any morning flights, so we have plenty of time for the transfer. It's best that the flight is after 5pm, please get in touch if you are in doubt before booking this flight.
Kefalonia airport connections