South Africa is very economical compared to other regions of Africa and it also has the added benefit of being Malaria Free, and no Yellow Fever Vaccination is required like East Africa.
For game viewing I recommend you head north west from Johannesburg approximately 3hrs by road transfer to Pilanesberg National Park there is a variety of accommodation options. The Pilanesberg National Park has a great variety of wildlife including the big 5. I have visited this NP twice and we had great sightings of White Rhino, Elephants, Lions, Zebra, Giraffe, Impala, Leopard, Cheetah, and Wilder beast just to name a few. It is worth spending three nights at a lodge located inside Pilanesburg NP with the option to do the morning and evening game drives.
The next destination I recommend is The Palace at Sun City, it is a very impressive resort with great options for the kids and adults alike to enjoy. There are several swimming pools including a very impressive wave pool. There are zip lines and rides, a shopping mal with many food options for those fussy eaters. From Sun City you can also enjoy a game drive into Pilanesberg National Park, or go for a hit of golf on one of their world class courses.