About 20+ minutes steep walking, just slightly east to the town centre, is this monument. The pen-like object points to a plate underneath which is the symbolic geographical centre of New Zealand. It's the tiny white/blue spot on this map. The real geographical centre is a little further south. More info here.
On this day, I saw bunch of primary school kids coming with teacher and parents to learn how the Maitai River flows to the sea.
This is on your way up. Here is a view from the top.