indepedent travel in East Africa

My wife and I are planning our first trip to East Africa, with a likely itinerary including trips to Uganda or Rwanda, Tanzinia, and/or
Kenya. We like to go off the beaten path, and we enjoy ourselves more when we don't have our hand held everywhere.

We're trying to get a sense of how much independence we can get away with and still be reasonably assured that we'll get the experiences we're hoping for. Obviously, we're planning on something in between the extremes of an all-inclusive trip and just showing up and booking things on the fly.

We'd like to hear from experienced travellers who, like us, enjoy independance and are used to relying on their wits. How conducive is
East Africa to this kind of travel?