Coles, Woolies, Big W, Target, Kmart, Aldi all have trolleys that require coins or tokens to unlock them in the ACT, but also in Vic, SA, WA QLD and NSW . I suppose it depends on the city.
We rarely use cash but also do not pay the surcharge for using the card very often. The reason for this is where we shop and how we use the credit card, of course cash or debit card do not attract the surcharge.
It looks like there are several car hire places about 15-20 Min walk away or back by the ferry terminal. You may better with a cab from the drop off point.
You cannot walk off the dock in Wellington, you need to get the shuttle (free) which will take you into the city. The drop off and pickup spot is on Lambton Quay close to the corner of Whitmore Street. The Beehive is across the road.
We are very modern in in the ACT, we have things called flyscreens, they fit in front of / over doors and windows and keep out the flies, mossies, beetles and a multitude of other bugs.
Once you are off the dock and in Lyttleton, you could also walk it, it is a fair hike but it saves some money as well as walking off the ship's breakfast.