I would suggest East Africa.

You can start in either NBO or ADD, both of which have good connections to other continents (DAR, KGL, EBB can work as well ex-EU). You should then be able to combine Ethiopia, Kenya, Tanzania, Rwanda, Uganda (Burundi too, but may be more challenging). At least for many EU citizens, these countries either have Visa on Arrival or E-Visa systems that are reliable. In the case of Kenya, go for VoA as otherwise you don't get a passport sticker.

Connections between the countries are plenty, with ET and KQ having major networks, while there's a number of smaller airlines as well flying both between the capitals and regional cities. Besides that, there's loads of fascinating destinations, even if you're only in each country for a few days. ZNZ is also a fantastic destination that can be combined easily.