Just outside Pointe Noire, there's the spectacular Diosso gorges. One can negotiate a taxi for the day to go there and forth. Local village boys have barred the route to the lookout point and ask about FCFA 2000 pp for entrance.
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Housed in a former royal palace, displays artifacts (weapons, baskets, etc) pertaining to tribal life and the history of the region of the Republic of the Congo.
Jane Goodall's chimpanzee sanctuary for rescued primates who have been caught up in illegal bushmeat trade. May be able to arrange tour.
Musée du Cercle Africain de Pointe-Noire
A great repository of African masks, plus sculpture and painting. Souvenir shop is on the premises too.
The premiere beach of Pointe-Noire with pretty sand but a little bit contentious as far as surf, theft, and safety (at night) go. Be careful going barefoot too due to broken glass.
A five-hour drive (in the dry season) North of Pointe Noire, near the Gabonese border is the vast and relatively scarcely visited national park of Conkouati-Douli. Elephants, gorillas and chimpanzees can be seen here. Be sure to strenuously ask your guide to do a tour of the Ngongo river as late as possible and to go down the river with the engine turned off to see elephants and gorillas.