I went through the non Schengen list of countries in the Europe, neighboring countries and former Soviet republics and for South Africans here is the list
Romania - Visa required or can enter with multi entry Schengen visa up to 90 days
Bulgaria -Visa required or can enter with multi entry Schengen visa up to 90 days
Serbia - Visa required or can enter with multi entry Schengen visa up to 90 days
Bosnia - Visa required or can enter with multi entry Schengen visa up to 30 days
Croatia - Visa required or can enter with multi entry Schengen visa up to 90 days
Albania - Visa required or can enter with Multi entry Schengen visa up to 90 days
Montenegro - Visa required or can enter with Multi entry Schengen visa up to 30 days
Kosovo - Visa required Can enter with Multi entry Schengen visa up to 15 days -
https://aab-edu.net/en/about-aab/we...lication-requirements-procedures-guideliness/
Moldova - Visa required or can enter with Multi entry Schengen visa
http://www.mfa.gov.md/entry-visas-moldova/foreign-need-visa/
Georgia - No visa required can stay up to a year
Turkey - Free 1 month e-visa online
Ukraine - Require visa from Ukraine embassy in SA
Russia - No visa up to 90 Days
Crimea- Currently part of Russia, was part of Ukraine
Kazakstan - Need visa from embassy in SA
Madedonia - Can stay up to 15 days with multi entry Schengen visa
Azerbaijan - Need visa from embassy in SA
Armenia - Can get visa at airport or apply e-visa
http://www.mfa.am/en/visa/
Belarus - Need visa from embassy in SA. Namibians and 80 countries don't require
Tajikistan - e-Visa or Visa On Arrival
Turkmenistan - Visa required
Uzbekistan - Visa required
Kyrgyzstan - Can get visa at airport
So basically if you have a multi entry Schengen visa it gives you a lot of options as long as the total doesn't exceed 90 days for all the countries combined that you use the visa.