The airport of Kythira is located on the northern side of the island, about 20 km north of Chora. The official name is Kythira Airport Alexadros A. Onassis. This airport receives flights from Athens and few charter flights from other Greek islands in summer.
There is no public bus outside the airport of Kythira island but there is a taxi rank. Passengers can take a taxi to transfer them to their destination around the island. Alternatively, many hotels in Kythira provide transport from/to the airport to their guests.
In order to make things easy, you can book your hotel.