Kia ora,
I am in Gisborne NZ which is north of the Hawk's Bay, but it is a nice region too. We have some caches as well and lots of nice landscape. You can't search with zip/postal code. The best is to use local names like Napier Hastings Waikaremoana and it will show you the caches on the map, The last name is also a very pretty place and in the very heart of the NZ bush.
If you ever come to Gisborne, come and say hi
Have a safe trip
Cheers
nzkeko