Qantas is offering return flights from Auckland to Tokyo from $753. These flights go through Brisbane for a short stopover before heading to Japan.
Next best price appears to be from Hong Kong airlines at $850ish however requires a 9 hour layover in Hong Kong. The other Chinese airlines are similarly priced & with similar long layovers.
Skyscanner + Google Flights can help you with the dates although it's not pointing out the correct fares on the calendar.
Dates:
27 April - 10 May
16 May - 30 May
23 May - 30 May
06 June - 21 June
08 June - 22 June
13 June - 21 June
13 June - 28 June
20 June - 28 June
06 Aug - 27 Aug
07 Aug - 21 Aug
07 Aug - 14 Aug
07 Aug - 20 Aug
