All the way back to the early 1900s, Kenya, Tanzania, Ethiopia and Southern Africa have been very popular.
Ethiopia offers a remarkable culture, with stunning nature. Kenya is "pole pole" - take it easy. Tanzania has of course Zanzibar and Mount Kilimanjaro.
Southern Africa (where I happen to live) is in comparison to the above destinations relatively "boring". Adventure is to be found up North; but adventure means "unexpected", so be prepared for that. If you don't like the "unexpected", go for Southern Africa.