There are five flights a day from Kagoshima serviced by Japan Air Commuter. Takes 30 minutes. Book in advance for cheap tickets. There are also one flight a day from Fukuoka and Osaka.
Toppy and Rocket Jetfoil
A good option if you can catch the earlier boat and arrive before lunch for more time to explore. The timetable changes slightly from summer to winter. There are five or six boats daily. The earliest boat leaves Kagoshima port at 7:30 arriving in Miyanoura at 10:30 and the last leaves at 15:00 or 16:00 arriving in Anbo depending on the time of the year (one-way/return ¥9,200/¥ 16,600).
Best way to get here if you are not pressed for time. Leaves Kagoshima Port at 8:30, arriving in Miyanoura Port at 12:30. Go out on the deck and enjoy the view of the island as you arrive. No reservation necessary for foot passengers. The return ferry for Kagoshima leaves Miyanoura at 13:30 arriving at Kagoshima Port at 17:40 (one-way/return ¥5,000/ ¥9,500).
The cheapest option, yet getting to Taniyama Port where it leaves from is a bit of a hustle. Leaves Taniyama Port at 18:00 and arrives in Miyanoura at 7:00 the next day spending the night at a port in Tanegashima (one-way/return ¥3,000/¥7,200). The bus for Taniyama Port leaves Kagoshima Chuo Station at 15:48 arriving at Taniyama Port at 16:34.
Taiyo Ferry (for Kuchinoerabu Island)
Kuchinoerabu Island is an island with a population of just under 100. It’s part of Yakushima Town and only accessible by this ferry run by the town. Leaving Miyanoura at 8:25 on even days and 13:00 on odd days. The trip takes about two hours with a spectacular view of Yakushima Island from the sea. The ticket is 2,140 yen one way.