There is good hiking in Hong Kong (albeit in pretty murky air most days) and, I believe, some around Tokyo, but not so much (the place for hiking in Japan is Hokkaido). Singapore doesn't really have any hiking or nature (except the zoo / night safari) - you'd need to go over the border into Malaysia for that.

Singapore is probably best for the quality and variety of food; Tokyo is expensive for non-Japanese food; Hong Kong is somewhere in between.

Macau would be worth a 1-2 day side trip on the ferry from HK for the Macanese food, and the bits of culture that haven't been turned into casinos.

Mandarin isn't much more useful in HK than English, and English is clearly the first language in Singapore. I find Tokyo quite hard to navigate as a tourist without Japanese, but others seem OK with it.

Obviously there are many places in Mainland China where there is good hiking/nature, but the food side would depend rather on your definition of "good". Your Mandarin would be a definite asset, but you'd need a visa.

Taiwan is another option. There is plenty of hiking in the central areas, which would again be facilitated by your Mandarin. There are good restaurants around of various types of Chinese and also Japanese.

I wouldn't try to do to much. Do you mean 14 clear days between arriving in Asia and leaving Asia or does that include the day in each direction going transpacific? In 12 real days I'd probably just go for two centres (counting HK/Macau as one). In 14 I might try to get in three.

That was a bit of a brain dump. Not sure if it is useful...