Visiting the north of Grande Terre can be a great adventure and we heartily recommend a road trip!
Our best advice is to get a rental car, drive up RT1 to Koné, then cross Grande Terre via the scenic Koné–Tiwaka road (RPN2) that winds through the mountains to the Tiwaka river mouth, 14km north of Poindimié. From there, head up the wild east coast via Hienghène, cross the Ouaïème River on the three-car ferry, then carry on north. After Balade, you'll then cross back over the island to Koumac. It's then a choice of heading up into the far north or, with less time on your hands, back down the coast to Koné.
The roads are in excellent shape – if you stick to the main roads, the only place you'll hit an unsealed road is the last 5km to Relais de Poingam in the far north, if you decide to go that far.
Allow three or four days and do some exploring!