New Zealand shops have to have a licence to open Christmas Day and they must sell 'essential supplies'.
Christmas Day and Boxing Day are public holidays and tourist attractions will be closed, certainly on 25th.
As here, restaurants are booked months or weeks in advance for Christmas Day lunch.
This is a good site that lists the best attractions and provides email addresses for each. You could email for opening times to help you plan your holiday
http://www.leadingattractions.co.nz/Default.as px?DN=5,1,Documents