Air Hawkes Bay or Air Gisborne would be my first options, knowing what I know now. Would also seriously consider Waikato.
Reason #1 - value for money. Both place require their intructors to do air ambulance (i.e. short-notice anywhere flights with sick people). Excellent value having "this-is-what-I-did" in the right seat instead of "this-is-what-I'd-do".
Reason #2 - Cost overall. Air Hawkes Bay has a good simulator and a good system to use it. They'll let you in gently in single-engine PA28s for the basic Instrument Rating then the Multi-engine endorsement removal, so your brain has time to adapt, also keeps the cost way down. Air Gisborne is inexpensive but not "cheap", also both Gisborne and Hastings are pretty cheap to live in (and you can live on-site at Hastings). Think half the rent of Auckland, and maybe 30% of the day-to-day travel. And the beaches are less crowded.
Reason #3 - CONTACTS!!!!! There's a lot of East Coast people in a lot of airlines reading this...
Reason #4 - work - as mentioned if you time it right and fit the 1000hr B-cat mould, you'll be welcomed. Some other experience is also nice like charter, tailwheel etc. but insurance dictates quite a lot.
Good luck with the search and remember it's YOUR money.