The Arusha Savannah is the largest savannah at AKL. You will see animals from your balcony there. To get a view of this savannah you have to reserve an "Arusha Savannah View" room. If you're interested in club level, the non-DVC club level rooms also look out on this savannah even though they're called "standard view" club level rooms.
If you reserve a "Savannah View" room, you will get a view of one of the two smaller savannahs - Sunset Savannah is one, and I think the other is called the Pembe Savannah though I can't remember for sure. You will also see animals from your balcony if you're in these rooms, too.
There are different animals in each savannah (though I think at this point there are giraffes and zebras in each - someone will correct me if I'm wrong, as it's been a while since I stayed at AKL). We've had rooms with views of the Sunset Savannah and the Arusha Savannah, and seen lots of animals from each room.
There are also pool view rooms (with views of the pool or foliage around the pool) and standard view rooms (usually views of the parking lot, but sometimes you can luck out and get a room with an obstructed view of the savannah). If you reserve these rooms, there are lots of public lounges and outdoor areas to view the animals.
There is a thread on this board all about AKL, with a summary about the resort at the beginning. I have no idea how to link to it, but it's usually in the first couple pages of the resort board, and is entitled something like "Number 9 is really fine."
I hope this helps!