It does depend a bit which route you took. Tracks I can think of between those places:
Hutt Valley Model Engineers Society….on the beach at Petone, two tracks but not a folded loop.
Paraparaumu…Kapiti Miniature Railway. Their layout is quite complex, and the track does pass over itself.
Palmerston North Model Engineering Club. Their track was only just getting underway in the eighties
Wanganui (Now Whanganui) used to have a club and a track, I don't know if they still do.
New Plymouth has a track New Plymouth Society of Model and Experimental Engineers.
Hamilton has a track, Hamilton Model Engineers.
Rotorua used to have a track, that society now has their track in Cambridge (NZ)
Napier has the Hawkes Bay Model Engineering Society.
There is quite a nice track in Tauranga, that got started in the late seventies and has now developed to have both ground level and raised tracks.
But most of these are not on the direct route between Wellington and Hamilton
John