The Raqqada National Museum of Islamic Art sits just outside Kairouan, near the site of an Aghlabid palace city. Its collections are a strong complement to the Great Mosque: ceramics, coins, carved stucco, glass, metalwork, and manuscript pages that show the refinement of medieval Ifriqiya.
The museum is especially worthwhile if Kairouan has made you curious about more than mosque architecture. It gives detail to the dynasties that shaped the city, and the quieter location outside the medina makes it easier to slow down with the objects.