Had a dig through Thailand fares for the next few months and late October is clearly the sweet spot. It's the last stretch before high season kicks in from November, so prices are still low while the weather is already turning good.
Auckland to Phuket, NZ$494 one-way (Jetstar, 1 stop) on 21 and 28 October. Cheapest clean fare I found anywhere in Thailand from NZ.
Auckland to Bangkok on 28 October, take your pick:
NZ$560 Hainan Airlines, 1 stop
NZ$658 Jetstar, 1 stop
NZ$668 China Eastern, 1 stop
Three different carriers on the same day is handy if you have a preference on airline, timing or baggage.
Wellington to Bangkok NZ$709 (Jetstar, 2 stops) on 14 October if you're not flying out of Auckland.
A few honest notes. These are all one stop or more, there is no direct option from NZ. Everything above is a single ticket, so your connection is protected if something runs late. I left out the cheaper looking self transfer fares on purpose because those are separate tickets and you wear the cost if you miss the connection. Jetstar fares are seat only, so add bags at checkout. Krabi and Chiang Mai were poor value from NZ right now, and Christchurch had nothing worth posting.
Link opens the search with the route loaded and prices in NZD. Full disclosure, Sky Spy is my own free flight search, that's how I found these. Happy to run other routes or dates for anyone.
Might kayak back.