The most popular places for South Africans to emigrate to are Australia, the UK and the USA. If you plan to stay on the continent, Nairobi, Kenya and Windhoek, Namibia are also good expat destinations. Where do you have your eye on?
Keep in mind that almost wherever you go, you will need some type of visa or work permit. In most places, you will need to already have a job in order to apply for a visa or permit, or you will need to prove that you have enough money to support yourself financially. So step number one should be to find a job, and this could help you decide on a destination. Will you be working too?