The Hlane Royal National Park in Eswatini (Swaziland) is one of the best parks in Southern Africa for tracking elephants or rhinos by foot.
It is free when you have a Wildcard.
Elephants, rhinos, lions, leopards and cheetahs, giraffe, zebras, as well as some antelopes. See African flora and fauna for information on animals.
Go on a guided bush-walk in the northern part of the park (guide is E20 per hour). This is the best way to get close to elephants and rhions on foot. The sighting of a rhino is nearly certain.
Ask to be shown the tiny Scops Owl that roosts at the main camp.
The park is ideal for children. It is small enough to navigate, large enough to explore, no guarantee of what you will see, but pretty certain to see impressive wildlife. Combine with the nearby Mlawula nature reserve (more dramatic country, less dramatic wildlife, campsite has outdoor showers with view over miles of mountain scenery) to please all tastes.