Athens airport and the ferries at Piraeus are far enough apart that the transfer has to be a planned hour, not a hope. A lot of Greek holidays are built as: land at ATH, cross the city, catch a boat. Metro and buses exist. They are work if you have time and little luggage. They are a bad idea if the ferry is this afternoon and the flight was late. A pre-booked car from the terminal to the port, or to a hotel if you are staying in Athens first, is the version that survives a delay.
Kiwitaxi is one of the firms that sells that ride at a set price, including larger cars if there are several of you and hard-shell bags. Piraeus is a working port. You want to be there with margin. Island timetables care about wind more than about your hotel check-in. Missing a ferry in July can mean a full day, not forty minutes.
Once that connection is honest, the rest of Greece is a choice. The mainland and the Peloponnese are buses, hired cars, archaeological sites that are hotter than the photograph, and towns that empty at midday. The islands come in groups. The Cyclades are the postcard. The Dodecanese sit toward Turkey. The Ionian side faces Italy. Ferry infographics that show every island as a hop ignore how few boats actually run on your day. Pick one group. Athens is worth nights, not only a corridor. Greek is the language; English will get you a menu on the famous islands. Cards have spread. Cash still helps on smaller boats. July and August are heat and competition for every bed with a view.