I'm a transplanted American living in Joburg, as everyone says, June is a great month but can be cool. I'd also say there is never a bad month, what you see changes from month to month. The summers are spectacular. I'd also say not to be afraid of driving, I've been on worse roads in New Mexico, the only precaution is to not drive after dark. If anyone is in Joburg for only a couple of days, a great day trip to go see the big 5 is to Pilansberg NP, right next to Sun City. I've actually had better game viewing there than at Kruger, but the feel isn't the same, there is a magic to Kruger which i've only other experienced in the Sergenghetti.

Cape Town is a great weekend getaway as well though I don't know how much fun it would be without your own transportation. Vic Falls is also fun, I went on my own and then organized a couple of tours after I got there, which to me was better and cheaper than going on an organized tour.

Durban / Umhlanaga Rocks is another great getaway if you want a few days of lying on the beach on the Indian Ocean. Haven't been there in June but it never gets too cold there, unlike the highveld. Do bring a hoodie if you come in June.