All of January is busy as its mid summer and many local people & Australians take annual leave holidays. Queenstown/Wanaka area will be busy and the Nelson region (Nelson, Ruby Bay, Motueaka, Takaka and even Collingwood) is busy with NZ'ers taking a summer beach holiday. (I go to the Nelson area to family at that time of year)

Jan/Feb will OK but finding and paying for accommodation may a little harder mid-end January. Not a reason not to go. Just do it.