From left field, It is pretty simple. Only air space you have to worry about in that direction is Tauranga. They are pretty relaxed.
Another option is heading North Bound from NZAR up the coast to NZKK. Get fuel there and then continue up to the top of the island and back down again. From memory that is about a 2-3hr flight around the top and back to KK.
Can always stop in at Kaitaia if you need to stretch your legs.
Stop in at Whangarei on the way south for some food and then the last 45 minutes or so back down to NZAR.
Its all in uncontrolled airspace. Only bit you have to look out for is the zone slightly north of Auckland but if you follow the coast below 1000ft, you are clear of that too.
If you get lost you can climb to around 3-4000ft and see both coasts... so its pretty easy to navigate around.
A few ranges that are around 2-3000ft, but they are inland for the most part, so if you are following the coast it should be easy.
This trip is a lot longer. Expect a full day. The coromandel trip is a bit shorter and has better stops. Then north one has a lot of scenery packed into it.