Depends on how long you will be around, but just out of Chch is the Hurunui, short but fun class 3-4 flow dependent. Then south out of town is the Rangitata, class IV, fun but kind of a haul still a good day out though.
Then from here you get into Murchison- lots of class 4 and Maruia falls good to practice falling or boofing or plugging or whatever.
The coast (west) has heaps of rivers that range 4-5+ so you just need to catch the flows right. Then the glacier runs are good further south near Franz Josef and Fox Glaciers, fox is the only one worth doing. Then queenstown has the Kawerau river and some others.
go to rivers.org.nz and look at the guide, it is all there that you would find in the book, but I suggest buying the book.
also paddlerzone.co.nz rents gear.
Send me a PM with your details and I will try to get you more info. February is going to be full on for me with teaching and work, so I won't be able to be your full time guide but I will try to point you in the right direction.
How long are you in CHCH?