Hi there 
The Wizard's Retreat is the main store in Christchurch. They host (as far as I know) the only FNM, and run the Prereleases and other tournaments. Chris, the owner, is a good guy, and runs good tournaments.
The store has room for about ~60 people to play if you really pack them in, but FNM isn't usually that busy
Larger tournaments are run at the Bridge Club instead. The store has a good range of boosters and singles, as well as plenty of people in trading.
They are open Wednesday-Saturday; can't remember the hours off the top of my head, but late night is Friday, for FNM, which as far as I know is Draft every week.
There are a few other stores that carry cards; Comics Compulsion on Manchester Street, and (I think) Chalon Stamps and Coins on Gloucester Street, though I haven't been there in a long time.
Hope that helps; any other questions, please feel free to ask!