Avoid leaving valuables in a vehicle no matter where it's parked - the worst places to tempt fate are tourist parking areas and the car parks at the start of walks. While crime isn't a huge problem in Wellington it always pays to take sensible precautions; don't leave your valuables lying around.
Don't underestimate the risks posed by NZ's unpredictable, ever-changing climate in high-altitude areas if you leave Wellington to go tramping. Make sure you let people know if you are going on overnight or longer walks, plan carefully and bring plenty of water.
The North Island's byways are often made hazardous by speeding locals, wide-cornering campervans and traffic-ignorant sheep. For a safer trip onward from Wellington, set yourself a reasonable itinerary instead of careering around the country at top speed, and try to stay alert on the road despite the distractingly beautiful scenery.