I have not found any locations within the city that I find quiet. There is always the presence of excessively loud (muffler-less or deliberately made to sound like it) cars/motorcycles, parties that stretch well into the next morning, musician neighbours having regular jam sessions, drunken singing in the street at 4am, fireworks at all hours, cars blasting music, peeling tires... it's always something.
I don't live in Palermo, but I've had occasions when I spent time in one of the clubs; looking out of the window at the nearby residences I always wondered about the training one must have to go through to become desensitized to that level of constant noise.
My area (Villa del Parque) is not known to be noisy, but it's noisy.