A large district between the airport and central Johannesburg, Sandton is known in popular culture as one of the richest areas in all of Africa; a fact made all the more ironic when you consider that the long destitute neighborhood of Alexandra is just to the east. If you're splurging on accommodations, you'll be here, where the shopping centers are huge and glamorous (Nelson Mandela Square and Sandton City are extravagant) and nightlife and dining options are plentiful.
Everything is pricey in Sandton, so head out to Melville or even into downtown or Newtown if you're looking for cheap cocktails and dancing space. There are some great hotel bars and dance clubs in the Sandton City area that look out on upwardly-developing skyscrapers, while a taxi ride down Rivonia/Oxford Road will run you aground of numerous shopping centers that more than likely will having reputable drinking and dining.
The Rivonia neighborhood has a few nightclubs, galleries, and even a local theater, particularly around Rivonia and Witkoppen Roads. Big clubs in the district include Manhattan Club, Eden, Taboo, Movida, and Icon while restaurants in the area tend to be more expensive and aimed toward the more developed palates. Molecular gastronomy, anyone?