RodH: Further nitpicking, the IDL is the 180 meridian which runs north / south to the east of NZ (besides some wobbling for geographic convenience around the mid and North Pacific) and its southern end is at the south pole . Within Antarctica, that runs (True) south through the Ross Ice Shelf, which puts it about 190nm to the (True) east of the Scott / McMurdo bases. The South African base is actually near the Prime Meridian... the 0 degree line of longitude on the opposite side of the continent. It and Troll, (at just over 2° W and E respectively) are closest to the prime meridian but this has no relevance for the start or the end of the "day"!
I have it on good authority that folk at Amunsdsen Scott base at the South Pole do stand on the dateline and play time travel games, especially around NYE.
Oh - Did you factor in the NZ time is GMT+13?