On North Island the best riding spots are:
Woodhill (near Auckland)
Rotorua
Craters of the Moon (Taupo)
42 Traverse
and Wellington (my personal fav but I live there so I'm biased)
South Island
Queen Charlotte track (closed for the peak season in summer)
Nelson area
Craigieburn (though this is much better in winter for skiing)
Plenty of stuff around Christchurch
Wanaka/Queenstown even though the chairlift uplift has shut at Coronet Peak.
The Kennet Bros book is a good place to start, also have a look at http://www.tracks.org.nz and http://www.vorb.org.nz
If you want to hire a bike of half decent quality you'll struggle outside of Rotorua, Welly, Chch and Queenstown. I think there is a place in the Abel Tasman area that has good bikes and offers a package of a couple of days riding and accommodation. Loads of backpackers type places hire out some rather suspect old bikes which are fine for a gentle pootle along some flat trails but I wouldn't fancy taking them anywhere remote or technical for the most part.
I've heard good things about Fat Tyre Bikes in Queenstown. Gregg who runs it is a well experienced biker and will tailor trips dependent on ability.