You should bear in mind that many of the iconic African mammals are not indigenous to the Cape. Most of the game reserves in the area stock many such species (e.g. giraffe, white rhino, impala) anyway, which makes them king-size glorified zoos.
The exceptions are the National Parks (e.g. Addo-Zuurberg, Mountain Zebra, Tankwa Karoo, Bontebok, etc.) and the private Bushmans Kloof.
Johan