I know you say your heading North from Christchurch but if you happen to stop by Queenstown Vertigo Bikes are awesome!
http://www.vertigobikes.co.nz/In April I booked onto their Heli-Biking trip however it was too windy for the chopper to land so it got cancelled

The heli-biking was booked for the last day I was in Queenstown so Instead I did their 'Gondola Downhill Tour' which was 2 runs of the DH track on a Giant Glory, it was a blast

The guide was also really cool.
If I was going to Queenstown again I wouldn't bother with the Gondola DH, it was great fun but I think the other 2 trips (Heli-Biking or Skippers Canyon) would allow you to take in more of the beautiful views...
I spent quite a few days in Nelson on the North tip of the South Island and am certain there would be some nice biking there! The city was surrounded by hills and there were a couple of nice bike shops although I don't know anything about renting bikes in Nelson.