Gombe Stream National Park is the smallest of Tanzania's national parks whose nature you experince on foot with all your senses. The steep slopes and many lines of river valleys around the northern silvery shore of Lake Tanganyika is inhabited foremost by chimpanzees. These will forever be associated with the pioneering spirit of primatologist Jane Goodall. She founded a behavioural research programme in 1960, which now makes it the longest-running study of its kind in the world. Most of her fieldwork was done at Gombe and because of this, it's a great place to see chimps up close as many of the family groups are habituated to humans.
There are other primates at Gombe. Red-tailed and red colobus monkeys stick to the forest canopy but a troop of beachcomber olive baboons, under study since the 1960s, is also habituated.