"Motorways" are not legally accessible for pedestrians. You very occasionally see hitch-hikers standing at the motorway end of on-ramps but that's definitely illegal. I've heard tales of people being given rides by friendly off duty or plain clothes police and taken off the motorway. I don't know what the fine is but i'd guess in the $200 region - and I may be wrong.
A motorway has a formal definition, but you know them when you see them. No side roads - on and off ramps only and usually 100 kph with some 80 kph zones in 'selected areas' - such as entering Auckland's inner city "spaghetti junction" where Southern, Northern and North-Western motorways meet to party - it is only a pale imitation of eg LA's motorways but is complex enough to merit driver attention.
The Auckland Harbour Bridge is a motorway but also forbidden to pedestrians in it's own right.
Some of the newer main highways use divided carriageways and in a few cases the eg North and South sections take different routes across country - eg portions North of Hamilton. These are AFAIK "just highways" and hitch-hiking would be allowed. some of these can be somewhat fast and furious and sense should be used as to where you stand.
There are a few roads which look motorway like but are not. These are termed "limited access roads" - they do not have vehicle access from adjacent properties, but road junctions may or may not have overpasses or similar. eg the first part of the road from auckland airport towards Onehunga is a limited access road. After a while it turns into a motorway, once the airport industrial belt is passed. I'm about 99% sure that you ARE allowed to hitchhike on a limited access road BUT vehicle stopping opportunities are limited and danger levels higher. They are usually short enough (usually maybe 2-10 km?) that you probably will not find yourself in the middle of ine.
Apart from motorways I can't think of anywhere else that is illegal.
Karangahape Road in Auckland at the Western end at night is probably a very bad place to try and hitchhike from if you do not want to be badly misunderstood (even if you are male) - but it's not illegal.*
It's probably legal to hitch-hike on "The Skippers Road"!!! but you'd need to be awesome brave and certifiably insane to do so, although most who do survive.
This is very obviously off the core topic but almost related. I think it should be interesting and maybe useful, but, if admins or anyone else feels badly enough about it just delete it.
*. In a prior corporate lifetime I used to work nearby and would quite often leave the office late at night, with the shortest path to the motorway taking me across K Rd and down through the back streets behind "The Pink Pussycat". Late on almost any freezing winter evening poor souls with impressive high heels and hair do's and a fraction of the attire that the cold merited would wave hopefully from the shelter of doorways. Sad the hand that some are dealt. I've not driven through that area at night now for many years, but maybe relatively recent NZ law changes have altered the necessity for such bitter means of customer contact.