If overseas visitors only have a week in New Zealand’s South Island, I would recommend that they prioritise visiting the Otago Lakes, Queenstown, Te Anau, Milford and the West Coast. But there is so much more to see! If you do have more time, or you’d prefer to go places that are less touristy I have a few suggestions for you.
From Dunedin you can hire a car and drive 1.5 hours south to the Catlins, the hidden gem of Southland. It has an unspoilt dramatic coastline with magnificent coastal cliffs and headlands, long sweeping beaches, coves and sandy bays, as well as rainforest, waterfalls and rolling farmland. You’ll see New Zealand’s beautiful native forest as well as lots of native birds. Along the coast line you see fur seals,sea lions and Hector’s dolphins, and if your lucky Yellow-Eyed Penguins. The main township is Owaka which has an information centre. There are tours you can take, or with maps and brochures in hand, you can be your own tour guide. There is accommodation to fit different budgets in Owaka and around the area. Ideally you’d want to spend 3-4 days in the Catlins.
Further south another native wonderland is Stewart Island, a ferry boat ride or short flight from Bluff, the South island’s southern-most town. A hiker’s and hunter’s paradise, you can do walks (we call them “tramps” from a few hours up to 8 days! There are many activities you can do such as kayaking, diving and fishing. Stewart Island’s township is called Oban and has accommodation for different budgets (but best to book ahead as there is finite accommodation on the island). Most visitors take a day trip to Ulva Island, sheltered within Stewart Island’s Paterson Inlet. This is an open sanctuary which is vibrant and noisy with native bird song. At dusk you may even see Kiwi birds on the beach!
Another option for an extended stay in the South Island is to visit Nelson and the Abel Tasman National Park at the top of the island. If you were coming from Christchurch you could drive up to Nelson via the Lewis Pass and the Nelson Lakes. If you were coming from Wellington you could fly to Nelson, or catch the ferry over to Picton and then rent a car and enjoy the beautiful drive to Nelson. You could base yourself in Nelson or closer to the park in Motueka or Kaiteriteri which has a stunning beach. The drive from Nelson to the beginning of the Abel Tasman National Park is about 1.25 hours but no doubt longer as you might stop off at one or two wineries along the way 
Abel Tasman National Park is incredibly beautiful and there are a number of options for enjoying it. You can hike the whole track over 3-4 days or, if you only have one day to spare you can catch a water taxi up to gorgeous Bark Bay and walk back to the Marahau end. I have done this day trip and I thought it was an absolutely gorgeous walk: through native bush, along golden bays and across river estuaries. I love coastal walks and this is one of the best. Another popular option is kayaking tours of the park. You camp on the beach if you are on the park overnight. How good is that?!
Finally if you’re in Christchurch and you’ve got an extra 1-2 days up your sleeve, I’d suggest you drive up the east coast to visit Kaikoura. Amongst other things, you can observe fur seals and pups in the wild and/or go on one of the popular whale watching tours. Kaikoura is also famous for it’s fresh seafood including delicious crayfish.
