In South Africa this past January, I was driving my rental car in one of the parks and two rhinos came up along either side of us on a dirt road. You literally could reach out the driver window and touch one, and the passenger window and touch the other (we didn't.... but we could have).
It was both awe inspiring and terrifying as there was no way out and I didn't want to startle them. They have really poor vision, so a loud noise like an engine starting can spook them.
They were chill, though I wasn't chasing them.
On the elephant side - maybe our best sighting of the whole trip was like 15 minutes into our first day in Kruger, self driving and a few elephants stumbled into a pack of sleeping/resting wild dogs. Elephants running between cars and trumpeting, dogs coming out of all the bushes barking. It was chaos.
I did have one momma elephant start to get agitated as she decided to turn and cross the road where I was parking and watching her and her calf. Nothing too scary but I got my ass out of her way.
Self driving safaris are wild. Though the off road ones (dead giraffe with lions around it, Hyenas stalking a leopard den to try and eat a cub, rhinos sparring) can show you some really crazy stuff.
Anyways, go to Africa, it's great.
