Fasting, shabbos, praying, and any other time-dependent mitzvah always goes by where you are right now.
I'm still searching for more sources on this - but I have never heard any halachic authority say anything different on this issue (with the exception of sfiras haomer, but for a reason that only applies to sfiras haomer)
This idea is mentioned on Young Israel's website, without citation.
There are even websites that help you to calculate what time the day (and therefore the fast) starts and ends, while you are in mid-air!
This is helpful not only on a fast day, but for any day, to figure out exactly when to pray on the airplane.
If one were to board tonight's El Al flight (Jan 4, 2012) from JFK airport in New York City at 23:50, he/she would land in Israel after a 9 1/2 hour flight, where the time would be 17:15. on Jan 5.
The fast does not begin until sunrise on Jan 5. Assuming one sleeps for the first eight hours of the flight, one would only be awake for the last hour or so of the fast (10th of Teves) - since the fast ends, according to the latest opinion, at 17:30.
Is it worth the $1,100 roundtrip ticket to effectively skip a fast day? Maybe for some very wealthy and frail people, it is.