Christianity is actually split on which day to keep. Those that follow the Catholic Church (via canon 29 of the Council of Laodicea) worship on Lord's Day[1] (Sunday). Those that feel the church could not change the day of worship (e.g. Seventh Day Baptists) worship on the Sabbath (Saturday).
Wikipedia has a small breakdown for the 7th day in http://en.wikipedia.org/wiki/Sabbath - some going with local, some going with time in Israel. Not being Jewish, I am not sure how accurate this one is for Jews: http://www.star-k.org/kashrus/kk-trav-dateline.htm
It was my understanding that Catholics go with local to determine Sunday.
[1] http://en.wikipedia.org/wiki/Lord%27s_Day