For a sample of what Zimbabweans eat in some form, nearly every day, ask for "sadza and stew." The stew part will be familiar, served over a large portion of sadza - a thick ground corn paste vaguely like polenta and the consistency of thick mashed potatoes that locals eat at virtually every meal. It's inexpensive, quite tasty and very filling.
If you want to really impress your African hosts, eat it how they do: take a golfball-sized portion of the sadza in one hand and kneed it into a ball, then use your thumb to push a small indentation into it and use that to scoop up a bit of stew before popping it into your mouth. Don't 'double dunk'.
For extra credit, clap your hands together twice gently when it or anything else for that matter is served to say, "Thank you." Believe it or not, they'll be very impressed.