There’s quite a bit going on within an hour or two’s drive of Christchurch. Any of the following make a great daytrip:
To the west are the Southern Alps, featuring hikes in Arthur’s Pass National Park and Mt Hutt Ski Area.
Head north to the Waipara wineries or the hotpools at Hanmer Springs.
Drive south, then east to Banks Peninsula and Akaroa.
Or if you don’t want to venture far afield, Lyttleton and the Awaroa/Godley Head Walk are close at hand to the southeast.