Definatley pack your bikes away on your campervan or inside the car...NZ is safe enough but i wouldnt leave mine unlocked or on back of car for long...
Not suitable for road bikes but if you can hire hybrid or mountain bike, you should go on Central Otago Rail Trail from Alexandra to Middlemarch... its awesome! Then catch steam train to Dunedin :-) google for website ....
Theres another rail trail that goes from Christchurch to Banks Pennisula - i assume it wasnt affected by earthquake in February
Enjoy... makes sure you book things in advance....january is summer holiday time and places will be busy....