Teaching English in Taiwan is a wonderful alternative if you want to experience traditional Chinese culture - as it intersects with Western modernism - yet feel teaching English in China isn't for you.
Taiwan, once known as Formosa (I know this from my childhood stamp collection), isthe 'other China', the one mainland China is always threaten to invade and reunify. Ties have become closer over the years, but there are still two Chinas, for better or for worse.
This is a more offbeat destination, not on the usual backpacker trail across Asia, yet you'll find everything you usually find in many parts of Southeast or East Asia: great food, lush rainforests, fabulous beaches and cities that buzz with nightlife. People are welcoming, possibly in part because comparatively fewer Western tourists make it there. And don't forget the hot springs!
You can look for a job or a place to stay before getting to Taiwan through one of the many recruitment agencies on the web or through English-language classifieds, some of which are listed in the Resources section below. One of the best web resources for teaching English overseas is always Dave's ESL Cafe.
Or, you can wait until you arrive. There are several English-language newspapers with classified ads, and they are crammed full of teaching jobs. Another of my favorites for classifieds is Craigslist. Your hostel should have a bulletin board, and fellow foreigners should be able to give you a few pointers as well.