The Earnslaw Burn Track in the Glenorchy area of Otago is a challenging tramping track that takes you through bush to a stunning viewpoint with views of an icefall on Mt Earnslaw/Pikirakatahi. The 8.3 km one-way track requires advanced tramping skills, with river crossings and route finding essential. Camping is allowed at the forest edge or Rock bivvy, but not on private land. Be prepared for severe weather, river crossings, and windfall along the track. It's a tough one, so make sure you're up for the adventure before setting off!
The other option is to fly in by helicopter with Heliworks Queenstown (which is the option I was lucky enough to choose).
For photography, definitely take your wide angle lens (16-35mm or similar) and your zoom lens (70-200mm or similar). My advice is to explore down the small river, get right up to the waterfalls, and make the most of all the different compositions available. It is best to visit during daylight hours as sunrise and sunset are both in shadow due to the surrounding mountains.