What's the Eye of a Hurricane called in Chinese/Pinyin?
It's 风眼(feng1 yan3) or 台风眼(tai2 feng1 yan3), simply the word-by-word translation to the English word "Eye of (the) Hurricane/Typhoon".

You can see it on the wiki: http://zh.wikipedia.org/wiki/%E9%A2%A8%E7%9C%BC