All of the south island! Depends on the whinging level of the kids as to how far they will walk. Presuming they are like my nieces of the same age they wont hike 1000m up a hill.
Second Castle Hill area. Kids explore while bouldering. And Takaka/ Paynes Ford where heaps of seaside and hinterland strolls with easy access climbing. Wanaka which has the kid inducement of Puzzling world. The walk to Aspiring Hut in the Matukituki is fairly flat but at about 10km probably too long for the attention span of a 6 year old. Arrowtown kids will like the museum and lolly shop and old goldmining huts. Seal colonies - there is one at Cape Foulwind on the west coast, and if the blowholes at Pancake Rocks are working they are very spectacular (there is climbing and a nice small beach at Charleston between these areas). Caitlins are quite stunning(no climbing though except at Colac Bay a bit further west). Cruises on Doubtful or Milford Sounds.... Stay at Homer Hut and walk up the Gertrude valley.
Just avoid earthquakes and rain and you will find heaps to do.