I agree about staying in Maboneng.
A day ticket on the red tourist bus was R170 when I was last there and you can cover a lot of ground and see heaps.
https://www.apartheidmuseum.org (understand that it is owned by the Gold Reef City Casino group).
Soweto has changed a hugely since 1991. Tours typically don't put a lot of money into local hands, but it's worth seeing.
Top of the Carlton Centre has an amazing view. Was R15 last time I was there.
Origins Centre:
http://www.wits.ac.za/origins/
Constitution Hill is lovely to walk around, and there are several walking tours of downtown Joburg.
Walter Sisulu Botanical Gardens has a lot of amazing African plants and a surprising number of bird species and other wildlife. The Montecasino Bird Gardens are amazing.
There are surprising numbers of parks nearby that you can walk in.
The reputed violence and danger are real, so take normal security precautions. Remember that 1 in 5 people you walk by have HIV.
It's an amazing city in a beautiful country. Enjoy.
Marty