I would presume that you would be looking to visit game reserves in the northern part of South Africa (Limpopo) where the main reserves are such as the Kruger National Park.
With that in mind, I would suggest either going during the dry winter months from May through to August where game viewing is at its best. However, the wet summer months (from November to March) are also a good time if you would like to see newborn animals and very lush, green vegetation which attracts migratory birds.
The only problem during summer is that it can get extremely hot. However, when you visit South Africa you are sure to have a great time on safari no matter what time of the year it is.
In terms of visiting Cape Town, if you wish you can have a look at my blog, http://journals.worldnomads.com/thea, where I have written about what to do and see in and around Cape Town. Hope it helps. almost 8 years ago
marty, Thea's advice is spot on. I did Sabi Sands (part of Kruger) in September and it was perfect.
Here're some safari safety tips for you
If you're going to Kruger consider one of the privately-owned reserves attached to it (but not fenced off). This is because in Kruger proper the trucks have to stay on the roads and tracks, whereas in the privately-owned reserves they can go anywhere they want while following an animal. Either way it's an incredible experience.
Phil from the safety hub almost 8 years ago