About an hour's drive inland from Port Elizabeth, Addo is home to 300+ elephants. It's a malaria-free park that provides viewing of black rhino, Cape buffalo, lion, zebra, even the revered dung beetle (found almost exclusively in Addo), in addition to the exciting elephants.
A tour through the 490,000 acres of Addo is either self-guided with your own car (preferable if you have kids under 6), or as part of a paid game-tour (for kids 6 and up).