Here are some dot maps I found online. They really show just how packed and dense most black neighborhoods are. Whites have almost completely abandoned the central cities post-apartheid and overwhelmingly live in suburbs. There are often a fair number of blacks in white neighborhoods --- but absolutely no whites in black neighborhoods.
In southwest Cape Town, you'll notice all it takes is one tiny but heavily populated village to make the entire ward black, even if whites dominate most of the land area with spread out mansions. As far as I know, Sea Point is the only densely populated white neighborhood left in the entire country.
Link to 2001 maps:
http://datalens.org/post/35117601723/mapping-south-africa-racial-dividesLink to 2011 maps:
http://adrianfrith.com/2013/09/08/dot-maps-of-racial-distribution-in-south-african-cities
