For "up to the Banks Peninsula, pick up a car from Christchurch" are you picking up a car and then drive around/to Banks Peninsula?
March is good time, but will be a few days of inclement weather. Your 12 day loop will soon go. Average road speed will be low. Only a few miles of divided 100 kph/60mph highways in the mainland (~South Island)

Look at Kaikoura and the Blenheim wine region

https://www.kaikoura.co.nz/
https://www.newzealand.com/au/featur...s-in-kaikoura/

https://www.scenichotelgroup.co.nz/b...n-marlborough/
https://www.airnewzealand.com.au/des...-food-and-wine

Invercargill (may not interest you)
https://www.transportworld.co.nz/