As a less than athletic individual I managed to have fun without hiking or riding a bicycle. I might have been able to have fun for $250 a day! In fact, you can have fun just walking around, going to the markets and looking at the beautiful architecture that almost blends in with the mountains.
While you are there, make sure you do something that might be a little harder to stomach. While South Africa is often over looked because it has taken such strides towards equality considering the end of Apartheid there are still a lot of fundamental inequalities in the country. Namely, education is still suffering. Go visit the townships, and try, as hard is it might be, to not act like a tourist and to actually see the way people live (I recommend not wearing a big camera around your neck and taking pictures of strangers). Go to small restaurants and talk to people, they are very friendly and the food is just as good as the nicer restaurants (none of which I've ever been to) that the article boasts. Go to Robben Island and listen to the personal story of your tour guide, see where Mandela slept, and try to wrap your head around a complicated history. Leave the city and see what the country side is like. It is much cheaper to stay in a single room along the backpacking routes than in Cape Town and equally interesting.
I know a vacation is supposed to be fun, but I find it impossible to imagine visiting this historic city without taking in some of the reality of life in South Africa. There is beauty and pain in South Africa and it would not be fair to yourself to not experience a little bit of both.