Well what do I say about my country. Yes there is crime but if you are aware of your surroundings and take basic precautions, you should be fine. Travelling alone in South Africa will be easy but requires a bit of driving as the public transport is not very extensive. I have to say that great strides are being made in this regard.
South Africa is beautiful and the people are warm (in my opinion anyway). In eleven local languages, there is no word for stranger!!!! It is extremely diverse and every part offers a different view of Africa. One week is not enough to see the whole land so pick an area and concentrate on it. A great place to start is the province/state of the Western Cape of which Cape Town is the capital city. You should have tons of fun.
If you need any help, let me know and I will definitely try to advise if I can. Happy planning!!!!