As far as famous hollywood stars there's not many from new Zealand, and the ones that are, were all born in or around Wellington, or atleast studied there.
Not sure why they need some Hollywood celebrity anyways...
As far as NZ male actors there's Karl Urban and Antony Starr, Temeura Morrison, Jemene Clement and Taika Watiti, but all hail from around Wellington, only morrison from rotarua.
Sam Neill at 74 is the only actor that's from South Island Christchurch, he is probably the only actor that has any affiliation with both the area and hollywood and has been off for the past year due to him having chemotherapy for blood cancer which in now in remission, so there's a good chance its him