When to Come to Tanzania 

The Tanzania National Parks offer wildlife viewing year round. Most tourists visit during dry seasons when wildlife flock to the waterholes, offering optimal scouting. The dry seasons last from December to February or March, then again from June to October. 

The second dry season of the year is the most popular time to visit as the air is at its coolest. However, this is also the time of year that hotels and lodges are most full and airfare is most expensive.

You can save considerably and enjoy having more things to yourself by visiting during a rainy reason. 
It may be more difficult to catch views of wildlife, though, because they typically disperse when rains begin and vegetation flourishes.