There is indeed a place called Kyoshi Island in the Nickelodeon anime "Avatar." However, this appears to be an "Asian-inspired" creation and not of Japanese origin. Furthermore, 'Kyoshi Island' would more than likely be a fictional name even if this were a Japanese production. Still, if you are a diehard fan and want a Japanese rendition, I would go for 'Kyoshi-tou'.

www.tvtome.com/tvtome/servlet/EpisodeGuideSummary/ showid-28841/Avatar_The_Last_Airbender/

You can also follow the links from the nick.com website.