Johannesburg — Joburg, Jozi — is the economic capital of South Africa and the largest city in sub-Saharan Africa after Lagos. It was founded in 1886 when gold was discovered on the Witwatersrand ridge, and the city is still built on the mine dumps that resulted; the endless low golden hills west and south of town are tailings. It is not a pretty city, it has a real reputation for crime, and yet it is the most important place in South Africa — where the politics happens, where the apartheid history is most visibly on display, and where the country's present is being worked out.
Downtown is rough, and most visitors avoid it. The middle-class centre of gravity has shifted north to Sandton, where the financial district, the Gautrain station, and most upmarket hotels are now. Rosebank is the next node north of the centre, with a big shopping precinct and the Sunday African crafts market. Melville and Parktown North are the bohemian restaurant-and-bar neighbourhoods. Maboneng is a small but successful regeneration project in the east of Downtown, with galleries and restaurants.
The essential sights are all about history. The Apartheid Museum is the definitive account of 1948–1994. Constitution Hill preserves the old prison where Mandela and Gandhi were both held, now home to the Constitutional Court. A township tour of Soweto — where the 1976 Soweto Uprising began — is the standard afternoon excursion; the Hector Pieterson Memorial and Mandela's house on Vilakazi Street are the set pieces. Further out, the Cradle of Humankind at Sterkfontein is where many of the most important early hominid fossils have been found.
Joburg is also the gateway to the rest of South Africa — two hours by air from Cape Town, four by road to Kruger National Park, an hour to Pretoria. Most visitors use it as a stopover rather than a destination, though a couple of days here is enough to make sense of the rest of the country.
Safety is a genuine issue, not just reputation. Do not walk around at night; use Uber between neighbourhoods; do not stop at red lights in rough areas; keep valuables out of sight in the car. Within the safer northern suburbs things are comfortable, but the city rewards caution.