Basically there is no bad time to go on safari in Tanzania. Whenever you go you will see fantastic wildlife. Like climbing Mt Kilimanjaro, when the weather is kindest it can get crowded but if you can go a little off-peak and cope with the occasional shower you will find quiet parks and amazing viewing.
December to March
This is the summer season in Tanzania. Temperatures are pleasant with an average high of 28°C and an average low of 15°C. The rains from early November to late March are usually scattered and localised and do not last for more than a few hours. All in all the conditions for safaris could not be better. The wildebeest are in the southern Serengeti making this a perfect time to catch the migration.
April to June
There is a chance of heavy rain during this period and showers can be expected for a few hours most days. Particularly during April and May the parks are fairly empty and accommodation costs are often quite a bit lower. However, this time actually offers the finest game viewing opportunities of the year. Wildlife concentrations are at their highest in the Southern Serengeti, and the landscape is a lush green.
July to November
The weather during this time is usually dry and sunny, although October to December brings the short rains to Tanzania. The grass dies back and more and more animals congregate around the permanent sources of water making them easier to find. Visitor numbers (and prices) peak in August coinciding with holidays in the Northern Hemisphere.