Going To South Africa

From next Tuesday (13th Feb) I will be in Cape Town for a week or so. As I've never been to South Africa before, any suggestions of what to do/see would be greatly appreciated.

My plans so far include the Robben Island museum, taking the cablecar up Table Mountain and probably having a look round at least one winery. Apart from that, I'm open to suggestions. As I don't have a credit card, however, I won't be able to hire a car, so if you could try to make any suggestions in and around Cape Town itself, that would be even better.