The climate in Kenya basically divides between a dry season from June to October and a wet season from November to May.
The best wildlife viewing is in the dry season when the bush is less dense and the animals gather around waterholes and rivers. The wildebeest migration on the Masai Mara is at its best between the end of July and the end of September.
The wet season has its own beauty with green landscapes, newborn animals and migratory birds. March, April and May are the wettest months, so naturally the best deals can be had at this time. May, in particular, can be a good, cost effective time for safaris in Amboseli or Masai Mara.