What we did in that timespan from Christchurch was get a train to Greymouth and then picked up a car, then South through Franz Josef / Fox glaciers, Queensland, Milford Sound, Dunedin, Omaru, Mount Cook area and then back to Christchurch.
The train journey was good and can be done as a return trip if that suits you better.
Kaikoura – we did not see any whales or dolphins but were refunded 80% of the boat ticket, we were clearly unlucky. North of the Island, Picton area, is supposed to be beautiful but we did not have time to get up here.
We travelled as two adults so did not have to consider little ones.