The ultra-distinct National Theatre holds fairly regularly performances - although obtaining a schedule can at times be difficult. The theatre is home to the National Symphony Orchestra of Ghana, the National Dance Company and the National Drama Company. A number of youth groups also operate out of it.
For smaller performances, check out the Accra Theatre Directory.
Accra offers a number of museums that chronicle the country's history and culture. The National Museum is by far the most impressive of them all.