After the Tasman Valley we decided to do the Sealy Tarns track, which consists of 2200 steps! And that won't even take you to the top of anything. It will give you very good views, though, and an excellent bragging opportunity.
Aoraki, the Maori name for the mountain, means something like "cloud piercer". And Aoraki is the peak you can see piercing the clouds in the picture above.
The day after I did the Hooker Valley walk, which leads to the glacier lake where you have a great view of Mount Cook. This is a flat walk, so there were a lot more people there than the Sealy Tarns track.
Taking the above picture was pretty hilarious. I set up my camera on self-timer, as you do when you don't have anyone else to take your picture, and this Chinese man told me he could help. I said I was okay, and he then proceded to show me a picture of me he had just taken with his own camera, without asking, to show me that he could indeed help. And that is how a middleaged Chinese tourist ended up taking my picture.