My recommendation would be to fly directly to Cape Town upon arriving at JNB. I'd stay 3 nights at Cape Town. Three nights will give you a nice amount of time to get a feel for the city, Table Mtn, Robben Island, Kirstenbosch etc PLUS some of the key surrounding highlights like the Penguin Colony at Boulder's Town as well as further along to the Cape of Good Hope.
After 3 nights in Cape Town, I would take a morning flight to either HDS or SKU depending upon which safari lodge you are staying at. For a shorter stay, such as 3 nights, I would maximize your time and pick a lodge in a private reserve, like Sabi Sand or Timbavati. There are lodges to fit most budgets and staying in a private reserve has a lot of benefits such as off road driving, night drives, and the guides are for the most part better trained. In addition, in private reserves, they communicate with other lodge jeeps for sightings and this means that you will get to see more even in only 3 days.
On your day of departure from your safari, you typically do the morning game drive then go back to the lodge for breakfast. After that, you gather your belongings and transfer back to the airport and fly to JNB. You usually get back to JNB around mid afternoon. Depending upon your actual flight schedule, you may have time to do some of the things you mentioned in Jo'burg but I'd recommend that, for a small price, you have a private car and guide to get you there and back in time for your evening flight. You don't want to miss your flight trying to squeeze in your last "To Do" items on the list.
A good tour operator can put these components together for you and you will pay exactly the same rates that you see online at lodges and hotels; ie there's no consulting fee.
Hope this info is of help.
Best
Dianne
Africa Direct USA