Things to see
The Musée Ethnograhique Barthélémy Boganda in Bangui is the country's national museum and has a decent collection of local instruments, weapons, tools, and displays about local traditions, religion, and architecture.
Prehistoric rock paintings can be found in several locations, but some of the best can be found in Bambari.
The "Chutes de Boali", a possible daytrip from the capital, are a rather picturesque series of waterfalls, which are even more impressive in the rainy season.
Megaliths near the town of Bouar are positioned in concentric circles and are remnants of the CAR's ancient peoples.
As with most of Africa, local markets can be a feast for the eyes, offering a wide arrangement of crafts. Just be vigilant, as markets in the CAR are rife with petty and violent theft.
Things to do
Visits and stays with the Pygmy communities are probably the biggest draw for the country's few tourists. Possible activities include: hunting with traditional weapons/devices, gathering medicinal plants with the women of the village, participating in a night of music & dance, and much more.
Visit the Dzanga Sangha Special Reserve to trek through the jungle in search of gorillas, elusive forest elephants, chimpanzees, & more. A visit to the reserve is often combined with a stay in a Pygmy village. The reserve is part of larger protected area, with Dzanga-Ndoki National Park (which consists of two noncontinuous parts: "Dzanga Park" & "Ndoki Park") flanking Dzanga-Sangha Special Reserve on two sides and which in turn is part of a larger, tri-national protected area including Lobéké National Park in Cameroon & Nouabalé-Ndoki National Park in Congo-Brazzaville.
Should the CAR ever emerge from the grip of conflict & dysfunctional government, the country would be an appealing ecotourism destination (similar to Gabon). Bamingui-Bangoran National Park and Manovo-Gounda St.Floris National Park are promising wildlife reserves that are currently in insecure regions and without facilities.