There is a host of guided activities on offer here but if you would rather soak up the grandeur of the scenery on your own then it’s easy enough to do so.
There are plenty of walking tracks in Aoraki Mount Cook National Park, from gentle, circular strolls that start and finish in Mount Cook Village to longer, multi-day hikes. There is also a one-hour walk along the Tasman Valley to a view point of the Tasman Glacier. From Lake Tekapo you can walk along the lakefront or take a more strenuous walk up in to the surrounding hills for lovely views back along the lake. Of course, the Church of the Good Shepherd provides one of the most famous viewpoints in New Zealand so if nothing else, make time to stop here.
The Sir Edmund Hillary Alpine Centre at the Hermitage Hotel is worth a visit, with great displays showcasing the history of mountaineering in the region and indeed mountain exploration the world around. There is also a theatre here which shows a range of 2D and 3D mountain-related short movies and doubles up as a planetarium whereupon you can learn about the magical New Zealand skies and galaxy beyond.
Down the road just outside Tekapo, Mount John University Observatory is a similarly good place for a stargazing experience (booking advised). Again, you can learn all about the southern skies as well as have a look through the powerful telescopes and see other equipment that is used for astronomical research.