We are a couple, sightseeing, modest accommoddation
I live in Wellington and I can safely say as I've done this trip in reverse that 4 days is plenty of time to drive this route! You can do it in one day in about 11 hours, with breaks and stops.
From Auckland I recommend travelling through to Hamilton and staying overnight in a hotel. You could go for a detour here and spend a half day at Hobbiton Movie Set which is a fun day trip. It can only be visited as part of a tour group. It's well worth it. I think most leave from Matamata township itself.
Travel down to Rotorua next, visiting Taupo and Rotorua which is filled with cultural fun. Maori displays and museums. Visit the mud pools. Rotorua Museum of Art & History is awesome to visit too.
Day 3 you could detour to New Plymouth and there's lots of cafes, art galleries and museums including the Govett-Brewster Art Gallery/Len Lye Centre which is a stunning piece of architecture in it's own right. It's an award winning building.
Day 4 an easy 5 hour drive from New Plymouth to Wellington. Although stop before you hit Wellington for the Hutt.
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