(Preamble: a two-year vet. I apologize for the length of this. I get really excited whenever anyone talks about NZ, I loved it so much I actually tried to emigrate there, lol.)
It's going to be hard hitching out of pretty much everywhere in the North Island except the two big cities (ESPECIALLY the East Cape, mostly just because there are seriously maybe 20-30 people per town and the road traffic that does exist is mainly in the form of tractors and JCBs) - and that's unfortunte since those are the areas in my opinion that are a really must-see. Māori culture out there is predominant and sometimes a little intimidating but they will probably take a shine to you just because you're obviously forging your own path and things.
It's a little bit expensive, but if you can swing it, I would suggest getting a hop-on/hop-off pass with one of the backpacker buses. They have kind of a frat house kind of culture, but you can choose to interact with the other kids, or don't and just treat it like a Greyhound. The advantage is that you'll be able to make it to those remote locations without having to hitch. I know that Stray (the orange bus) has a specific East Cape pass which might be of interest to you. It picks you up in either Auckland or Wellington I think. (Also, if you don't want to deal with backpackers at all, there might be some sort of Intercity bus pass, though I never rode them myself.) I also strongly recommend taking a trip to the far "Winterless North," and there is a specific Stray pass for that too. Paihia has a fairly robust funky/alternative scene, though mostly only in summer. (I worked there over the winter and there is a reason they call it "The Womanless North.")
In terms of a real arts, music and counterculture scene, Wellington is really where it's at. Auckland is pretty bizarre in that there's really nothing in the center of it, like at all. It's an incredibly vast place just in terms of sheer area and it can feel more like a big sprawling exurb than a cohesive city. (Though there are certainly some very cool pockets and neighborhoods, Ponsonby, K-Road and Newmarket being the trendier ones. Also there are several very beautiful nature reserves that are actually a part of the Auckland "city limits." Kitakita Falls has some excellent abseiling.) Wellington has much more of a local identity, is very walkable and is probably the most American-ish place, aside from I'd say Queenstown in the South Island.
As far as recommendations, I second the Raglan suggestion. Surf school is there, but almost even better is the local hostel...they have a nighttime zipline and you go zooming through pitch black rainforest and there are glowworms ALL over the place. I really, really urge you to check that place out. Once in a lifetime.
Tongariro Crossing is an obvious one, and another once in a lifetime thing. Just PLEASE make sure you pack for all types of weather, even if the morning is 75F and sunny, even if the forecast SAYS it's going to be 75F and sunny. My group set off into a lovely blue sky and by our second hour the rainclouds had gathered, gale force winds had picked up and the temperature plummeted. I was wearing jeans, sneakers and a light North Face windbreaker. I have never been so cold in my life. One girl in the group actually had to be med-evacuated off the mountian in one of those shiny silver hypothermia blankets. The weather up there is no joke and you want your memories of the place to be full of splendor and not misery. One of the best parts about the whole experience is the base camp hostel, which is a ski lodge in winter (gorgeous, gorgeous accommodation...like five-star level for hostel prices) and then the dinky backwoods little local bar, in I want to say Mangawhero?...I guess people are a little delirious after they do the hike because some strange shit goes on there. The bartender has this parrot that will sit on your shoulder...it's a trip.
Anyway...sorry to overload you with details. I dunno, for me New Zealand was a life-changer. I hope you find your niche there, and I'm certain you will. There really is no place like it on Earth. Every single type of terrain and ecosystem under the sun. And all in such a tiny little postage stamp of a country. It really blew my mind after awhile. You gotta just give it time and let it get into your bloodstream. It will.
