I'm not from Wellington, but have been there a few times.
One of the Cafes we frequented was Fidels, though I'm not too sure where it is. Possibly somewhere on Cuba st near Real Groovy. Also The Krazy Lounge (also on Cuba) is a good place to hang out if you want to people watch.
The City Gallery is good if you like that kind of thing, and if you like books there is a great bookstore, either Busy Bees, or Buzzy Bees. My memory isn't that great sorry.
You should head for Cuba St anyway, they have a lot of buskers and people hanging out who would probably know where any good bands are playing.
hope that helps some
All the best