been there, done that!! Last January.... I did three weeks on the North Island.
Feedback - the hills are like Devon and Cornwall but longer. Lots of 3-4-5km hills pretty steep. There are long hauls on busy-ish roads and several stretches which are long steep hills, lorries, narrow (eg Napier to Taupo)
I think for a month it would be hard to do both islands, but I think the South has more steady long climbs which are less steep.
WHere I went there was always a hostel or similar with a bed for £10 a night so I only camped when I had to. If alone and prepared to do a bit of planning the you could easily get away without camping kit
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... BUT in spite of any moans above I had a fantastic time. Really fantastic. See here for full info
www.crazyguyonabike.com/doc/nz and get in touch if you want a chat.