If a person was in Nairobi, Kenya in March of some year, what would be the easiest access to hunting, and what species are generally available?
Especially of interest would be cull/management hunts at cheaper prices.
No hunting is allowed in Kenya at all. Hasn't been for a generation. As far as i know, Tanzania is the closest destination with good hunting, and it is not a cheap country to hunt in. You might try further west, but those countries have some serious social problems.
As mentioned by castnblast, there is no hunting allowed in Kenya, and has not been since the 70's.
I would recommend flying into Zambia. I'm not a big fan of Mozambique. Saying this, there are some top outfits running from over there, in great areas.
Is Tanzania safe and stable right now? That looks like the closest place.
What is your budget? None of East Africa can be considered as a "bargain" or "cheap" in terms of hunting. Look at Uganda as an option. Tanzania and Ethiopia are not cheap in any sense of the word. I do not believe that any of the aforementioned countries offer "cull or management" hunts to foreigners but I may be mistaken on this point.
There are some tremendous hunting opportunities in that part of the continent but you will PAY through the nose.
I realize you mean big game, but Kenya does allow bird hunting. I know a couple people who've gone on bird shoots in Kenya in the past few years. African bird hunting is as good as the big game hunting, but would probably be considerably cheaper.