South Kivu's star attraction is this national park, where you can track habituated eastern lowland gorillas (Grauer’s gorillas) for just US$400 per person, a relative bargain! The park also contains a chimp orphanage at Lwiro (US$30 per person), where between 40 and 50 chimps are kept in excellent conditions.
It's often possible to get gorilla permits for same-day hiking, and never a problem to get them with a few days' notice. Lodge Co-Co is the best place to arrange a trip. The starting point is at Tshivanga, 30km northwest of town. Moto-taxis there and back cost about US$20 to US$30, while hiring a taxi costs US$80.
It's also possible to arrange guides at the park to take you on some excellent hikes up the mountains (US$100 per day).