Few have been to Africa’s largest private game reserve as it only takes few guests at a time - on 400 square miles! It’s the "Green Kalahari", which means arid savannah rather than desert - scenically magnificent, with rare species like desert black rhino and black-maned lions. You can get close to meerkats at one of their colonies. Don't expect abundant herds, it's too dry for that. The camps are very lux, with pools and a/c. South Africa.
Best time: To avoid desert extremes the shoulder seasons are most pleasant, March - May and August - October.
Access: Regular flight shuttle from Johannesburg (1.5 hrs)
Combine with: Kruger, Okavango Delta

I recommend these camps

Tswalu Tarkuni (5 suites) The Oppenheimer family’s own house on this vast reserve, recently redesigned, private and elegant – and share their love of horses by riding out amongst herds of sable and other antelope. Tswalu Private Game Reserve, South Africa. Private villa. Child friendly. $$$$$. Read more.
Tswalu The Motse (9 suites) Looking over the magically still “Green Kalahari”, this is unlike any other safari, indulgently luxurious with unusual activities like horseriding, walks, really long drives or sleeping out under the stars. There are 3 family suites which make travelling with kids easier. Tswalu Private Game Reserve, South Africa. Child friendly. $$$$$. Read more.