We opened our account at Kiwibank. It wasn't an online process and I did have to post the application along with copies of our passports and bank statements, but they were very fast and we've been quite happy with the service.
The account was opened 7 days after I dropped the application into the mail and we have just transferred some funds via XE.com.
We won't be in NZ for a while as we don't even have an ITA yet (but we're selected!), but this is something I could do now. Since this money is set aside for us to settle once we get there it still fulfills its purpose and makes me feel like I'm making progress now