Our next stop, after visiting the Mount Aspiring National Park, was the Mount Cook area with Lake Pukaki and Lake Tekapo. The area of Lake Pukaki is beautiful and the lake is really as blue as the pictures are showing, nether the less the place is packed. Only stopping there and hop off for a picture, might be OK but finding there some solitude is hard. I mean the place is popular as the filming location for The Hobbit and for that reason alone are many tourist at this place.
If you want to have a nice overview of the area and not getting the standard shot go up to the University of Canterbury Mt John Observatory in Tekapo. It is possible to drive up there or hike up there. The hike starts at the Lake Tekapo Motels & Holiday Park and is ~2 km one direction. Up there you can find the Astro Café, where you can sit outside and enjoy the view.
At Mount Cook we did the short hike Tasman Glacier View Track. It is a short hike of 2 hours which starts at the Blue Lakes car park and ends at the Tasman Glacier. As sadly applicable for all glaciers in New Zealand, there is not that much to see anymore of the glacier.
At the Aoraki Mount Cook Village you can find information about the area, hiking maps and accommodation possibilities.