If your main objective is to see large quantities of animals, then the easiest time of year to do this is between June and October (Tanzania's dry season). This is particularly the case in Ruaha and Selous in Southern Tanzania, Katavi in Western Tanzania as well as Mahale Mountains on Lake Tanganyika, although in June and early July the chimps can still be high up in the mountains.
The Ngorongoro Crater Highlands can still be full of flowers in June and July but be prepared for changeable temperatures, it being often cold with low cloud through these months. Tarangire in Northern Tanzania, which acts as a dry season refuge for wildlife from the entire Maasai Steppe is at its best for game between late July to late October, but is always good for elephant and in the green season (December to May) has tremendous birdlife.
The Serengeti and Surrounding Areas offers spectacular game viewing year round, so works a bit differently. Please, check the right time to visit the Serengeti with this linked webpage.
If the wildebeest migration is a major objective, then there isn’t really a "best" time to visit. River crossings happen between July and October on either the Grumeti or the Mara River, and the calving, one of the most spectacular times to visit happens in around February, with game action remaining excellent through March and April, before the wildebeest start moving off the plains during the rut in mid May.
If you’re traveling between December and May, then combining Serengeti Southern Plains and Loliondo is particularly important. The latter is a must if you’re interested in walking, night-driving and more of a wilderness experience.
People tend to overlook the green season months (Dec-May) in Southern and Western Tanzania, but between December and the end of February can be a great time to visit. Selous can become quite humid by January and February which makes it less good for longer walking safaris but everything is green and there are plenty of young animals and migrant bird species around.
Source from: http://www.naturalhighsafaris.com/content/the_best_time_of_year_to_visit_tanzania.html
