Tottori Airport is the closest airport with direct flights to Tokyo (Haneda Airport). ANA operates multiple flights per day. Flight duration is 80 minutes. The regular one way fare is about 31,000 yen, but by using a discount offer, you can usually fly for between 16,000 and 29,000 yen. Air passes for foreign visitors are even cheaper.
From Tottori Airport, Kinosaki can be reached in about two hours by rental car. Alternatively, take the airport bus from the airport to Tottori Station (20 minutes, 470 yen) and use local trains along the JR Sanin Line to reach Kinosaki (2.5 hours, 1340 yen, one transfer along the way).