I'm planning a road trip through both the North & South Islands. My style of travel is via rental car + campervan for 5 days in the south, with moderate budget (cheap to moderate hotels), with the length of the trip being around one month.
My first question is: how is the coverage for mobile internet at least along the major roads and towns in both Islands? I'd be using either Spark or Vodafone with my mobile.
Secondly, in the shoulder month of November, do you think that I can wait until last minute to book cheap hotel rooms? Is there an equivalent to lastminute.com or hoteltonight.com in NZ? Can I generally expect to find hotel rooms available during this month, or does wanting some spontaneity come with a steep cost?
You shouldn't have issues with mobile coverage in the major towns but do remember that New Zealand doesn't really have major highways excepts the one that heads south out of Auckland. A lot of the roads are single lanes, windy and often remote. In the South Island a lot of the roads are heading through quite mountainous areas and I do think you will have issues with mobile reception.
November is really the start of the tourist season as they have long cold winters but it doesn't really ramp up till school holidays kick in around the 18th of December. You should be fine to be spontaneous in the major places like Christchurch, Queenstown, Auckland etc. but if you do want to stay in some of the more isolated areas like Lake Tekapo you may have to hunt around a bit for accommodation as there isn't a large range to choose from.
I don't know of a NZ specific booking site but lastminute.com or booking.com should be fine to use. I don't think it will cost you to be spontaneous, it just may mean you miss out staying in some smaller towns where accommodation is limited.
Either one of those service providers have good coverage on all the major roads, Spark probably has slightly better.
You should have no problem booking in November.
Try Booking.com or Wotif, Expedia or any of the major apps I live in NZ and they are what I use.