It is in these areas that you are most likely to find species such as elephant, hippo, leopard, topi, vervet monkey, and baboon, to name but a few, plus a wide range of birdlife.
It can therefore be a smart move to visit these locations when the migration is not in town and visitor traffic is correspondingly low.
Generally speaking the weather in Serengeti national park is wonderful, but if you wish to travel in march, April, or the first half of may then you will probably need to put up with some significant adverse weather conditions. The whole period from November to February can also experience serious adverse weather, although this would be quite exceptional.