I've traveled to Eastern Africa (Tanzania) and Southern Africa (Botswana) for game viewing, and both have wonderful game view options.
If you can visit Eastern Africa to see part of the Million Animal Migration, that would be worth seeing. Be sure you visit the Ngorongoro Crater, a truly wonderful destination and my favorite place in this trip. The Massai tribe lives in and around the crater, and it's fairly easy to visit them in their villages (which your guide will arrange).
I do think the best gameviewing experience we had was in the Okavango Delta of Botswana. The private concessions here are worth paying a little more for because there are no hords of tourist. At most you'll see a few other people during the game drives, a very pleasant change from the National Parks in East Africa where dozens and dozens of Range Rovers can be seen around the rarer animals. Also, the guides in the private concessions are allowed to drive off road and get you closer to the animals, so you can see and photograph them better. It would be convenient to combine this with a visit to Victoria Falls or CapeTown in South Africa.
Our vendor for Southern Africa was 'And Beyond", the finest tour company I've ever dealt with. The entire experience was absolutely wonderful and their advice extremely helpful. Here's there link" http://www.andbeyondafrica.com/ There is no cheap way to get a great wildlife experience in Africa. It is expensive and as a rule you get what you pay for. That said, I think the finest travel experiences of my life were in Africa, with the African people, enjoying their wonderful wildlife! It's an experience you won't regret paying for.
If you're interested in reading more details and seeing some of the hundreds of photos from my experiences, please go to these links:
I'll follow the thread if you should have more questions I might be able to help with.