Crime in Southern Africa can vary from needing an armored vehicle to get around, to almost none at all. The problem is that unless you're local you can stumble into the bad areas without even knowing it. This can turn a pleasant drive, or walk into a nightmare that can even be life threatening. Having said that, it's more than worth the risk, and if you plan well, there is very little risk at all.
The most dangerous areas that most tourists are likely to visit are in the big cities. If you're going to be visiting any large city, the key is to know where you're going, and how you're going to get there. If you're driving or walking, make sure that you have detailed directions, and stay on highways and main roads as much as possible. Avoid travel at night, but if you are out at night make certain that you're aware of your routes to get around. Never travel with strangers and always make sure you're in a legal taxi. Making sure to keep your doors locked at all times, and parking in well lit secure parking areas is also a good idea.
If you're outside of the cities, sticking to main routes is still a good idea, so is traveling as much as possible during the day. In the countryside there's slightly less crime, however there's the added danger of wild animals, so stopping for a meal at the side of the road at night can be a little risky.
Small towns can also have their pockets of problems, but that really depends on what country you're in and what the economy is like in that town. Unfortunately poverty is running rampant in many Southern Africa cities and towns, and this can lead to crime. Lost tourists are a prize to desperate people.
Having said all of this, most people in Southern Africa are very friendly, from just about every economic level. You will likely run into some people trying to scam, or maybe even rob you, the trick is just extract yourself from that situation as quickly as possible, and head back to your hotel or a safe place ASAP.
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