I always recommend Thailand, good for all ages, in my opinion. Lots for kids to do and look at, food can be very palatable for tourists within tourist areas, inexpensive, and short flight. Xmas is also a perfect time to go, weather wise(but not koh samui side), but also peak season so a bit more expensive, crowded and usually need to book ahead.
We have been to Singapore and just now Taiwan with out toddler. No problem with both places, though sing would be better for smaller kids. Japan is fun, but coooooold in December (unless you ski), and within 4 hrs.