Hi, let me add a few details for the OP and others who might be reading this:
# Any ideas what is the best way to get there (Airline; easier via Tokyo>Okinawa, Taiwan/Taipeh>Okinawa or Tokyo>Ishigaki)?
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# Is it possible to get from Taipeh directly to Ishigaki via ferry or airplane?
"Yes" to the second question. You have the following flight options:
To Ishigaki Island:
- via various airports in Japan
... Tokio Narita / Haneda (transfer by train or bus required)
... Kansai airpoirt (near Osaka)
... Chubu airport (near Nagoya)
... Naha (Okinawa)
- via Taipei Taoyuan (Taiwan) (on Wednesdays, Thursdays, Saturdays, Sundays)
To Naha (Okinawa Island):
- via various airports in Japan
... Tokio Narita / Haneda (transfer by train or bus required)
... Kansai airpoirt (near Osaka)
... Chubu airport (near Nagoya)
- via Taipei Taoyuan (Taiwan)
- via Shanghai Pudong (China)
- via Hongkong
- via Seoul (Korea)
- via Manila (Philippines)
Tickets for the flight portion between Taipei and Ishigaki may not be available for sale in Europe - in that case i would recommend any of the routes that go through Naha (in my experience going via Taipei is the best in terms of time, on occasion also the cheapest. Going via Shanghai is quite often the cheapest.) Going via Tokio requires a change of airport, which adds cost and time. (We used to have passenger ferries between Okinawa Island and Ishigaki Island as well as Taiwan and Ishigaki Island, but unfortunately they have gone out of business.)
# What about known radiation in the water or the air in the south of Japan?
Probably like that you'd find in the waters off California or Hawai'i...
Many people think "Japan = radiation", but Fukushima is 2000km to the northeast of Ishigaki and water currents run from the south up along the Japanese coast to ultimately carry the radioactive pollution from Fukushima across the North Pacific in the directon of North America (of course, from there it
eventually comes - or has come - around to Hawai'i, the Philippines, and Okinawa). Radiactive airborne pollution related to Fukushima is probably still an issue in certain areas in Fukushima and Tsukuba, but not in Okinawa.