Yes, it is absolutely safe to hire a car. Remeber though that South Africans drive on the left side of the road.
I would suggest that you include a Navi when you rent the car.
I have used this website before to book a car: www.arguscarhire.com - it's a price comparison site, so you will get the best rate.
http://www.southafrica.info/travel/advice/driving.htm about 7 years ago
Also, renting a car will probably be your best bet since taxi fares are pretty high in both cities and public transport can be tricky to rely on.
Henrisan is right in his comment, you should definitely include a gps in your rental. Joburg especially can get confusing at times. about 7 years ago
I drove around Cape Town earlier this year on my own with no problem. Obviously apply road sense, don't get out to check your car if, at traffic lights, someone signals you to do so or you will likely be car jacked. I'm not sure that I'd drive around Jo'burg but didn't feel safe there even with my resident friends knowing where the safe areas are. Personally I feel there are better places to visit in South Africa than Jo'burg. It's a stunning country and there is so much to see. Enjoy it. about 7 years ago
Rented a car in Cape Town and drove to PE a few years back. That was easy and safe, but then we didn't drive too far off the well-worn tourist path (Garden Route).
It's best to keep the doors locked at all times to prevent bag snatching at lights or all-too-common car-jacking. Don't leave anything valuable in the car (especially not in plain sight).
If there's a self-appointed car park attendant offering to keep an eye on your car while you're gone - pay the 5 or 10 rand he asks. It helps him feed his family and probably works (it's good business sense for him to be reliable).
I didn't drive around Jo'burg, just picked up a car got on the main road out and headed for nice, more interesting parts.
Get some more tips from the safety Hub.
Phil about 7 years ago