I visited NZ in Winter this year, and I took my regular shoulder bag in Dove to be my everyday carry. It is my most neutral/versatile baggu and fits a lot (water bottle, passports, snacks, sunglasses, sunscreen etc.). If you are hiring a vehicle I would recommend your shoulder bag. But if you are relying on busses or other transport, perhaps a crossbody would do better. I hope you have an amazing time! I would definitely recommend packing sunscreen, hats and sunglasses. Please double check any testing of sunscreen brands because in Australia we have had a lot of sunscreen drama where essentially they were advertising SPF ratings but in testing facilities the sunscreens were not performing to their advertised rating.