I think Tauranga is one of the main fishing ports in the Bay of Plenty when it comes to charters, etc. I know someone who fishes out of there in our winter and they get tuna (yellowfin, SBFT) and mahi mahi around that time of year. Probably worth checking out charter options out of there.
I used to go to New Plymouth (west coast of the North Island) regularly and we did a charter with about 15 people from the office there at the beginning of April one year. Cruised out about an hour west in a large catamaran and jigged in about 300 feet of water. Caught all sorts,: red snapper (or at least NZ's version, seems everywhere has a fish they call red snapper), gurnard, yellowtail, some other things I can't remember and dogfish - they hate them even more down there than we do here. Didn’t have to wait long between bites, but nothing big so wasn't the most exciting fishing, but a neat experience.
One trip I saw someone come into the New Plymouth marina with a several hundred pound marlin in the back of their ~25' boat. Wasn't even close to fitting and it would have been fun watching them wrestle that in.
