The Ngorongoro Crater has a fairly temperate and dry climate although it can be extremely cold in mid-winter ( June and August) and so the question of when to go to the Ngorongoro Crater is an easy one: it's an all-year-round safari destination. This is underlined by the fact that the wildlife remains in the crater and there is little seasonal change in terms of game viewing.
There are two brief rainy seasons: one from April to May and again in November. Expect dramatic thunderstorms and short-lived downpours.
Note that during the main rainy season (April and May) the roads can become difficult - though not impossible - to travel on. This period is often seen as the best time to visit the Ngorongoro Crater as there are far fewer people at the Ngorongoro Crater. The traveller can expect large numbers of vehicles in the crater at other times of the year.