My wife and I are heading to New Zealand for about 4 weeks this Jan/Feb. I’ve been once but didn’t get to see a whole lot of the country. We have a couple days in Auckland at the start and we rented a beach house for a week near Tauranga as well. We want to check out the South Island some and farther north as well. Any suggestions on where to go and things to see? Thanks!

if you are visiting waitomo caves, let me know and I might be able to sort out a bit of hunting or fishing.

I live near Tauranga so I tend to take the local attractions for granted. PM me if you like. I presume you have already been to Rotorua. If not it makes a great day trip from Tauranga. Dont try and stay there. The Labour Government has filled all the motels with homeless people during covid. The top-end lodges are still OK. Unfortunately Rainbow Springs which used to be a top attraction for outdoors people with it's gigantic trout, has now closed. The geysers still blow in the thermal areas. Even this government couldn't stop that!
If travelling down the West coast of the South Island and you stop for the night at Franz Joseph to see the glaciers, drive out to the airport in the evening. Wild Chamois feed out morning and evening in the grass alongside the airport where they cannot be hunted.
If you go up to Mt Cook near Twizel there are Salmon farms in the hydro canals. The waste food from the salmon nets drops through and fattens the wild trout into the largest in the world. Not my taste in fishing but if you want to catch a 30lb trout that's the place.
If you go north of Auckland up to the Bay of Islands the Marlin will be abundant at that time.