Rain in Northern Tanzania mainly happens in the form of massive thundershowers, these by themselves are spectacular. Thundershowers normally take place in the space of one hour, cool down the air and give everything a new breath of life. It is rare to have rain for days on end.
Being seen as the 'low' season, lodges and camps all have great deals and a lot less guests travel to Tanzania because they believe this is not a good season to be here. Contrary to that belief, this is a great season. For one you get lower prices and have the whole place to yourself. But also everything is green, most animals are breeding and have young so the wildlife viewing still is outstanding.
The wildebeest migration is still in the vicinity of the short grass plains but some groups might be moving in to the central Serengeti and some into adjoining Game Reserves. So when designing itineraries during this time of year we will focus around the South and Central Serengeti.
Other parks: is a very good all-year park. It is a small park bordered almost on all sides; it is hard for animals to move out (although it's not like they want to move out with all the water and food there). So, for a guaranteed good wildlife experience visit this park any time of the year.
Similarly, Ngorongoro Crater is good year round. It does get very dry during some seasons but the wildlife is always good. Peak seasons (December/ January and July - August) can be very busy with other tourists.
Tarangire National Park is not too great at this time. Animals disperse over a huge area the moment it rains. The grasses also get very tall making viewing game hard.