Anfiteatro is small sector recently bolted on the north-east face of M.Pellegrino, just outside of Palermo. The area is very and panoramic and a quiet place to escape the buzz of the city. Great place for climbing in the summer, when you want to climb in a cool area in the shade.
From the centre of Palermo cross the Parco della Favorita towards Mandello. Proceed downhill for Viale Regina Margherita, at the traffic light junction turn right up the road (Via Monte Ercta) towards the S.Rosalia sanctuary. After a few kilometers, go through the second tunnel and park a hundred meters further along on the left. On foot walk back, and take a path to the left of the tunnel, that takes you to the base of the routes red signs). 10 minutes.
Palermo, you are just a the city limits.