Which Perth suburbs are most like Dunedin NZ?

Hi Perth-ites, Need your help... my husband and I are relocating from Dunedin NZ to Perth. We've lived in Perth before, way up north in Quinns Rocks many yeras ago, but it wasn't our cuppa tea at all. We'd love a suburb more like Dunedin, with heritage homes, really good coffee/cafes, and a cosmopolitan type feel (thinking of a Dunedin-Melbourne mish mash here). Any ideas people? Wherever we go, we'll be looking at the lower end priced rentals... I think Leederville would fit the bill. Any advances? Any help appreciated, Renee (mid 30s and looking to start a family sometime soon)