Driving in South Africa reminds me a lot of driving in Australia (if you've never been to Australia, then you can probably compare driving outside of cities in South Africa to be somewhat like driving in rural Arizona/New Mexico/Utah--think lightly-trafficked two-lane roads, except on the opposite side, which is easy to get used to). Driving in JNB and CPT reminds me quite a bit of driving in/through major Australian cities, albeit with significantly more visible pockets (or, sadly, really more like large swaths) of poverty, but you won't really have any reason to be in the poorer and/or more dangerous areas.

As far as safety in your car goes, use caution and be smart about where you go and what is visible (on you and in your car) and my impression is that the risk is reasonably low. (My experience is based on two visits and a sum of about seven weeks in the country and driving the breadth of the country from Kruger to Cape Town.)