Please, do not take it personally but my very first suggestion is to avoid to use a car. I just saw what goes under the name traffic on the Palermo roads and I walked faster than the average speed of cars or buses and the parking in the city center is simply not existing. And the local solutions decrease the average speed even more !
Villa Igiea should be a wonderful location, it was mentioned on my Michelin guide as a place worth to visit (Liberty itinerary) but it was really too far for a city break. Grand Hotel et des Palmes could be almost an ideal location.
[perhaps a main block nearer the teathers than Quattro Canti... but anyway, great location]