The Great Mosque is one of the finest Islamic buildings in North Africa and rewards closer inspection. Non Muslims are not permitted into the prayer hall, but the doors are open to allow you to view inside. Access to the main courtyard is available to all. The columns throughout the complex were taken from Carthage.
The Mosque of the Three Doors, has a one of the finest facades in Tunisia, though the interior is not open.
Medressas
There are several of these Islamic Schools in the centre of town that open up to visitors.Bi'r Barouta
this Well is the place where the city was founded, it is reputedly linked to the ZamZam well in Mecca, it is one of the holiest sites in the city for Muslims.Medina in general is a nice place to just wander around aimlessly, if it looks familiar it may well be as it was used in Raiders of the Lost Ark to double as Cairo.