Delta Airlines has dropped fare to Johannesburg, South Africa to as low as $710 round trip from Houston and Miami for departures in October and November. Fares in the $700s are available from August into April 2016.
British Airways has fare in the $790s and Star Alliance carriers are priced in the $750s. Fares from Los Angeles LAX are in low $800s. There are probably some other airports with these low fares.
Delta is the lowest fare at $709.40 round trip in economy V class with a transit through Atlanta.
$585 base fare earns 2,925 miles round trip for this itinerary in Delta Skymiles
British Airways has a $793 flying in economy O class via London Heathrow. The extra $83 will earn far more miles worth the difference in ticket price.
The routing from Houston to London to South Africa is more than 20,000 flight miles. British Airways economy O class earns 100% flight miles as redeemable miles in American AAdvantage. IAH-LHR-JNB-LHR-IAH is 20,908 flight miles. An extra $83 earns an extra 18,000 miles for a furutre ticket, plus you break up the flights with a few hours in London each way, rather than Atlanta.