There are two galleries inside the Sierra Leone National Museum – one housing a collection of cultural and historical artefacts, including Temne Guerrilla leader Bai Bureh's drum, clothes and sword; and another devoted to temporary exhibitions (at the time of research a fascinating collection of photographs and documents detailing the city's colonial past).
Entry is free in theory, but you'll likely be asked for a Le10,000 donation before entering; it is well worth it, considering you'll be guided around the exhibits by well-trained staff. The museum can organise guided tours of Bunce Island.