Te Paki Coastal Walk, Northland
Aotea Track, Great Barrier Island
Timber Trail, Waikato
Tarawera Trail, Bay of Plenty
Queen Charlotte Track, Marlborough
Hump Ridge Track, Fiordland.
I think the Te Paki Coastal Walk would be one of the frontrunners.
It has an established track and campsites, when I walked it 4 years ago, parts of the track were being upgraded to great walk standard already. To me this walk has the natural scenery and the cultural aspects required, it's relatively easy being walkable in 2-4 days, it's also in Winston's patch, the region has the infrastructure to support tourists, the region may need another popular walk in the area in case all the Kauri forests are declared off-limits. Also Te Paki connects onto the start of Te Araroa.
Can make cases plus/minus many of the above. Te Paki Coastal Walk, which I've done most of several years ago, as you say relatively easily walk-able, transport to from/it is a problem, which if it became a GW ought to help. No huts though, which puts many people off.
Which is ditto on a few of those,
- Tarawera Trail (which also is only a day walk, and the Hot Water Bay campsite gets quite full as it is, particularly with boaties - I often kayak there),
- Queen Charlotte Track again I think again has only campsites, also is on on Te Araroa? and so seeing more traffic anyway?
- Timber Trail looking at a link, looks to be an intermediate mountain biking trail (a la Otago Trail), so not immediately attractive as a walk.