I rented a car in South Africa and drove around. These are some of the things I safely saw from the driver's seat.

Doing a self-drive safari is probably easier and less expensive than you think.

Actually, the more time you spend in for example Kruger National Park, the better your deal will be. Buy an annual national park pass ("The Wild Card") instead of paying per day makes the average price per day go down. And with more time you can see more of this park and the sights than on a shorter drive. Kruger National Park is about the size of the country Denmark (not including Greenland!), so there is much to explore.

I'll be happy to answer questions you may have about how to do something like this.