Kia ora wannabe,
NZ is home for me, 40 years surfing most of it. Presumably you will hit NZ in November, which is spring time, and that means wind, and lots of it, predominantly from the nor west and sou west. Of course with wind at home, anything is possible! So for the north island that means east coast breaks will be lacking swell, as they require late summer east nor east swells. Gizzy and mahia will get some south swells, but the glamour waves are unlikely to be on - as a rule. So that leaves the NI west coast - tons of swell, typically 12 second period, but not often over 14, plus lots of short period swells, all from the south west. That means Ahipara, Raglan, Taranaki. And, the south coast of the NI, which has a great burst of south swell late October, early November, and certainly a road less travelled. The south island runs with a similar pattern - the west coats is WILD and cops the same sou west swell and wind pattern, plus rain, and well, more rain, especially in spring. The east - Kaikoura down to Christchurch, really needs east and nor east swells, which are more likely in late summer off cyclones, although big south swells can wrap in. Dunedin to Invercargill has a ton of south swell options, but the glamour breaks on the Otago peninsular also need swells off cyclones.
So 5 weeks, I guess you need to plan on which airport you fly into first, and where you depart from, and what temperature water you want to deal with after all that warm oz water! You also want to see if you can book your tickets within a week of departing oz, so you can make the call to start north, or south, depending on the weather, which changes all the time. My surf picks would be Dunedin / Otago - epic beachies, awesome town, lower numbers of van lifers, and lots of south swell, Taranaki, cause its home and it has a ton of wave options, and usually the van lifers stick in the same places cause they all use the same app, Ahipara because its warm, handles south west wind and its an easy drive to the east coast (but its a LONG drive from Auckland airport), and if the weather gods cooperate, the south coast of the NI. You gotta figure this one out yourself, but there are some gems to be had, and its easy driving from Wellington, which is an awesome city to hang out in.
But as I say, the weather changes - you might strike a big random east swell and get amazing waves at whangamata and other spots close by - anything is possible!
And please be careful in your van - visitors in vans are not loved by all (its the van accommodation with no self contained toilet that's the issue, not the people), especially when they park up in large numbers. Plan to stay in spots away from heaps of other vans. There are 50,000 tourists on an average day living in vans in the queenstown area alone - avoid!
Have an awesome trip!