The Gold Reef Casino has a good showcase of African dance. Don't look like a tourist - don't carry a camera around your neck or wear a moneybelt. It's easiest to get around with a called taxi. Spend extra money for a decent hotel in Sandton. The hotel also organises excursions.
Tours are a good, safe way of seeing the sights.
It is winter in July and August and cold at night. No rain though, so a fleece and jumper should do.