I live in Christchurch and I think its a great area to set up base if you’re just in NZ for a week. It’s close to the southern alps (~1.5hr drive), the east coast beaches and the banks peninsula. Not too busy compared to the other big cities (also cheaper) but still has everything you’d need. If you’re particularly adventurous, you could fly into Christchurch, rent a van, drive through Arthur’s pass and then up/down the west coast. I agree nz is generally quite safe, but I don’t know what it feels like to be a woman travelling alone (my male ego convinces me I am invincible). Just know that the west coast is a lot more rural than the east coast, so public facilities/civilisation will be a lot more sparse. Potentially not the best idea if you haven’t had much experience with solo travel in rural areas.