The Catlins Coast is as close as you can get to being 'off the beaten track' in the tourist-filled South Island. While you won't be the only one down there, you will notice the change of pace and isolation of the area. The locals are renowned for their friendliness and hospitality, so find a nice B&B or two to get a genuine local flavour.
From Invercargill, set off across the Awarua Plains towards Slope Point - the actual southernmost point of the South Island. you will also find the Petrified Forest and often dolphins swimming in the surf spot at Curio Bay.
The following day could lead you to Papatowai, or further on to Kaka Point. On this section there are several side walks to waterfalls or coastal beaches. From there it is not far further to Balclutha. For those who want to extend the trip, it is also possible to continue on towards Dunedin, via the Taieri Coast.