As I recall there was about a 15 degree (F) difference between Auckland and Tonga. Auckland was cool and rainy and I would guess it was around 60F. Tonga was definitely warmer.
The International Date Line is East of Tonga and we did not cross it all while on the boat. I don't know anything else about the IDL Hotel, but I would not stay there again unless they had complete extensive renovations.
Tonga is GMT/UTC +13 so it is one hour ahead of New Zealand.