I visited New Zealand twelve years ago and went in May which would be autumn down there, beautiful colours of the trees and not too many tourists about. I didn't do a bike tour but thought I would mention some places I liked.
North Island I saw Rotorua, hot springs, bubbling mud and geysers, the whole town stank of sulphur. I had a few days around Taupo area which I enjoyed. Wellington was worth a look and they have an amazing museum there, can't remember the name though! From Wellington I took the ferry across to Picton on the South Island.
The South Island is awesome, crystal clear rivers (at least they were then) and fantastic views seemingly around every bend. I stayed in the 'adventure capital' of Queenstown and visited the nearby quaint town of Arrowtown. Milford Sound was worth a look but one of my favourite places to stay was Wanaka. The Franz Joseph and Fox glaciers were also worth seeing assuming they haven't melted away by now! The area around Mt Cook is another wonderful place. Dunedin is ok and if I remember correctly it has the steepest street in the world, you may have to push your bike up there!
After your epic trip across America I don't think you'll be disappointed with New Zealand, it's a stunning place for scenery and well worth the long haul to get there.
