I live in South Africa now, with my wife and daughter, and while I could live in less than 1000 usd, it would be in dodgier areas of town. That said for a nice 3 bedroom pay ~700 usd, and food is like 250 per person. So from the sound of things, there are much better options out there.
Yes there are. Tons. I live in South Africa and feel completely safe. And I don't live in a security estate either. It's not as crazy as what you see on the news. It is however all about location.
Anywhere in the Western Cape, but I mean it doesn't just end there. I would be perfectly happy with many places in Johannesburg (like Bryanston), Pretoria, and also many rural locations.
That is not to say security is not a serious concern in many of these places, but you can lower the risk substantially by choosing the right neighborhoods etc.
Most of the crime happens in the dodgy areas (ironically - poor people suffer the most from crime).