We booked a hire car with Dohili tours = Lemy car hire by email and delivery and pick-up worked a treat. They have offices all over the island.
If you arrive in Ikaria by ferry and arrive in Evdilos, you might be able to get a taxi to travel to Gialiskari, which is approx. 20 minutes away.
The drive from the Airport to Gialiskari took approx. 1 hour 45 minutes by car.
When in Agios Kyrkos the best way to get to the north coast is to share a taxi with some other traveler, its cheaper (around 10 euros each) and faster, cause there are no real bus schedules and it takes for ages (around 1 hour) even in a taxi to drive to the other side of the really hilly island.
The taxi stop is near the restaurants on the left side of the harbour (facing the sea) next to the Kyoske and the bank.
To come to Ikaria, you have two posibilities: plane to Ahens and ferry from Pireaus to Ag. Kyrikos or Evdilos or plane to Samos (nearby island) in ferry to the Ikaria. Well... there is a third one - once a week there is a direct fly from Athens to Ikaria (Faros) airport but after seing this airport I surely dont advise you to take this third posibility.