Palermo: 4 nights (3 full days) would be great, including the visit at Monreale up the hill.
The area along the corridor Via Roma/Via Maqueda between the Teatro Politeama and the Quattro Canti is the best, and very safe. If you stay in that area but closer to the Quattro Canti, you will have to walk less to reach the cathedral, the Palazzo dei Normanni, San Giovanni degli Eremiti Church, and the old historical center.
I've never been to Bisacquino, but based on where it is, I think you have a better chance to find accommodations in Corleone, which is only 20 min away by car. Corleone, the historical capital of Cosa Nostra (the Sicilian Mafia), has become an international tourist destination thanks to the fame brought by movie "The Godfather". Don't worry about safety in Corleone. It's safer than any American city.