I lived in Takapuna for six months and used the Bayswater ferry to get the the CBD. While this service isn't as frequent as Devonport service, with the connecting bus service it opens up a wider area to look for rental properties.
http://www.fullers.co.nz/tickets-far.../bayswater.php
I found the Takapuna property (and later a bigger property in Campbells Bay) by visiting a couple of estate agents, collecting their daily list of local rented properties, reviewed the collected lists over a coffee in a nearby cafe and then returned to each estate agent to agree times to visit my selection. Both properties were visited on the same day and I moved in within a week.
As the rental list change daily then you may need to re-visit each estate agent more than once. Any half decent rental will go instantly, so be quick!
It helps if you have a car, a local map, a gps device and mobile access to the
www.maxx.co.nz website to check travelling time by bus. As the range or rental properties (and price!) will vary greatly, give feedback to the agent so they can help you with recommendations.
Finally, take a camera and don't be afraid to take photos of the properties during your visit.
Good luck!