Wikicamps is another handy app to find a place to stay. You may need to alter the strategy of only looking for somewhere at 5pm, that may cause problems, as cellphone coverage is not guaranteed outside urban areas. As others have said, a local sim can be obtained with data included.
I normally roughly plan the next day the night before, with maybe one or two bailout plans just in case. If all else fails I take a hammock and sleeping bag, and have found a stand of trees to sleep in, usually after dark. It's not really the done thing, so you should try to avoid that if possible, although on public land, such as Department of Conservation blocks you're less likely to get in big trouble. I take a shoe horn to dig and wipes for ablutions, which can also come in handy if the body becomes very insistent when far from facilities. Disposing of rubbish incorrectly is very frowned upon, packaging must be carried until a public disposal can be found, fortunately there are numerous of these, as well as public toilets in most small localities.
Another get out of jail card is to take a bike equipped with lighting, then if you get to dusk (9pm at this time of year) but still have a way to go, you can continue.
Department of Conservation maps:
Geocortex Viewer for HTML5
NZ topographic maps:
New Zealand Topographic Map - NZ Topo Map
Walking Access Mapping Service:
wams.org.nz
Other NZ advice: take mosquito repellent. Use sunscreen even on overcast days, the UV index in NZ is quite high, it's fairly easy to get burnt and the mild temperatures can decieve.