There are a couple of places to stay in Sidi Bou Said itself.
Hotel Sidi Bou Fares
15 rue sidi bou fares. right in the centre of town. all rooms are based around a pretty central courtyard. they are rather small, but are en-suite. single room rate oct '07 was 45 tnd, but it can be haggled lower.
You can easily find hotel rooms in nearby Tunis or Carthage. Additionally, if really lucky, you might rent a room for a night or two in a house, from a village resident. However, this is rare, since the locals are quite rich and rarely have any interest in sharing their home with total strangers.