Bearing in mind arriving so early, you can be leisurely going into downtown Auckland, not least because many things wont be open during the morning rush. The Skybus is fine (traffic is better since the Waterview Tunnel opened, but leave yourself plenty of time returning to the airport), you can catch it, go to a cafe downtown have a coffee and a decent breakfast (i.e. you could choose to sleep through breakfast on PER-AKL and eat downtown instead). You can buy a return ticket for the bus at the airport and use it to catch any bus on the way back.
After eating, drinking you can then wander around the shops, go up the Sky Tower, go to the Museum and get a ferry to Devonport and back. There are city bus tours, and you could ride the inner city orbital buses and get on and off along the way (although you'll need some NZ$ change to do so).
There is luggage storage facilities at the international terminal if you don't want to carry you hand luggage about all day.
The good thing is that if you get bored or tired, you just get the Skybus back to the airport, go through immigration and go to the lounge, freshen up ready for the flight to Vancouver. Do all that and you'll be ready for dinner on the flight and a good sleep through to Vancouver, which is only 3-5 hour time difference.