How much time should I spend in Christchurch? I have only 3 weeks to my trip and I really want to go there

Really?
Why?
Personally, I find christchurch a flat, grey, english-wannabee, conservative-pakeha borefest.
But if that's what floats your boat, knock yourself out.

OP, nothing wrong with Christchurch but its not a place where you'd want to spend heaps of time when NZ has so much to offer. If you plan it right, an overnight there would be enough. Ignore #1's rude response.

what are you interested in doing here and when? like other enzed cities christchurch is really just a gateway to most of the activities tourists would like to do.

I agree. no more than one day. It is worth doing a walk in The Summit Road and in the city center , but more than one day there for such a short trip is enough.
you can read more about Christhurch in:
http://www.triptouch.com/new-zealand/si/christchurch
but NZ have so much else to offer...