I was just in South Africa last year for 2 weeks. Spent about a week in Capetown, 3 days in Jo'burg, and a long weekend on Safari on Krueger. Capetown is hands down, the most beautiful city (in terms of landscape and geography) I have been too. Still, it's like a lot of other vacation spots and if you are at all interested in getting a real sense of what South Africa is like for those living there, Capetown will not easily give you that experience. The ride in from the airport, though, is an eye-opening experience.
As for myself, I was there studying/doing research so my experience with "touristy" things to do is a bit limited. Still, here are some ideas. .
In Capetown itself, be sure not to miss going up Table Mountain. You can be lazy (like myself) and take the cable car up or you can do a nice day hike up. The views down into the "city bowl" are stunning especially at sunset. A more adventurous way back down, is to abseil off the side!
Also be sure to take the tour of Robben Island. Tour guides are all former prisoners on the island. Boats leave out of Victoria Wharf.
Not sure how long you have, but around Capetown, there are lots of wonderful things to see and do. Renting a car might be a nice way to take any of the following in, though you can always arrange pre-packaged tours.
Among the things to see are Cape Point/Cape of Good Hope (which, contrary to popular belief, is not quite where the Indian and Atlantic oceans meet but is still beautiful nonetheless). I can't remember the names of the places off-hand, but on the trip down to Cape Point, there are two places people stop off at to see penguins and seals.
Another place, recommended by a friend, is Hermanus. You can go whale-watching and diving with great white sharks.
If you are interested in touring wineries, there are some excellent choices in Paarl and Stellenbosch.
You also mentioned Safari . . . the big park in South Africa is Krueger. I had a wonderful time. In just 2 days, we were able to see 4/5 of the big five game. Aside from doing typical night/early morning drives through the park, you can take bush walks with experienced guides. My one complaint about Krueger, though, is that it is a bit too overdeveloped and sometimes feels just like a really large zoo.
Have a great trip!