Westward bound LAX to CPT
If I recall correctly you can fly non-stop EZE-JNB and on to CPT if you want to visit South America.
Heading west from California, you can route yourself a variety of different ways. For example from Singapore you can take Singapore Air to CPT with a stop in JNB. Or you could go from SIN to IST or DXB then head south from there. It is not going to be a shorter trip compared to flying east.
There is a non-stop from JFK to JNB. Routing eastbound LAX-JFK-JNB-CPT is 11,233 miles one way. Routing LAX-NRT-SIN-JNB-CPT is 14,946 miles. It is still shorter to travel eastbound - look at the Great Circle routes (http://www.gcmap.com).
Also look into round-the-world tickets and fares.