If you find a good job there, you can apply for the job and have an interview and hopefully get the job and fly to Asia!!
Since I worked in Korea and China, I can tell you some of the pros and cons in Korea and China. If you want to go to China, you need to know that you shouldn't expect too much money. My friends couple went to China and taught English in a university, and they really received small money from the school. You will have a place to stay free of charge, and they will provide airfare for your air tickets if you keep one year contract. But, the salary will not be much. If you want to learn some Chinese and are very interested in Chinese Culture, you can go there and enjoy it there. However, you might not be able to save up at all. You can just say it was a really good experience. hahaha. China is a really big country and has so many fascinating thins to see and places to go. You will not regret it, but again, you will NOT SAVE UP MUCH. I went to Beijing, and maybe if you go to Shanghai, it will be a different story because Shanghai's living cost is much higher and they pay you more. So you can try to choose to go to Shanghai instead of Beijing. If the pay is similar, it might be better to come to Beijing because its living cost is lower than Shanghai.
If you have a education degree and hold a teacher's certificate, you might want to apply for international schools in China. There are so many international schools which are looking for teachers.
Korea can be a good option. It has a wonderful transportation system, so you will be able to go anywhere by subway or bus. Korea's food is quite good and healthy. Chinese food is quite nice, but it is quite greasy. I don't like greasy food, so I usually went to Korean or Thai or Japanese restaurants in China. And... the important thing is they pay you much more than China.
Some might want to go to Japan since they pay more than Korea. However, I just personally don't want to live there even though I want to visit Japan and go sightseeing because they have quite frequent earthquakes, and that freaks me out. I don't want to experience any earthquakes. I think visiting Japan is okay, and I don't need to go live there. lol. If you like Japan, you can go visit from Korea or China. I think that is enough for me.
Well. I think I covered quite a lot. You can research and find information on line and ask people around. Then, you should choose the place that you want to go by yourself.
I hope that this will help you. Thank you. :)