Mondello - 2 nights

This might very well be the best pizza in the world - I almost gave it 5 stars, except that I wouldn't want my last meal to be pizza.  It's what we Americans know as deep-dish or Sicilian pizza (despite the fact that not all pizza in Sicily is "deep dish"), and it basically melts in your mouth.  You walk in, and toward the back, past the biscotti and loaves of bread are various pizzas topped with seemingly random combinations of artichokes, prosciutto, mushrooms, fresh tomatos, etc.  Just point to whatever tickles your fancy, and they'll hack you off a slice and warm it up.  And it's cheap:  €2 for a hefty slice, meaning you can leave really full for less than €5.

If you want to escape the fascinating urban mess of Palermo, consider spending a night or two in Mondello (a 20-30 minute ride on bus 806 from Piazza Sturzo in central Palermo), and if you spend time in Mondello, consider staying at B&B Rosa dei Venti.  It's basically an immaculate and sprightly decorated two bedroom apartment, with each of the rooms being let out to guests (the proprietors live nearby).  Each room also has its own balcony and separate bathroom, and there's a kitchen for self-catering and large living room with satellite TV.  Food (and lots of it) is provided for breakfast, but you're left on your own in terms of actually eating.  €50 for a single, €72 for a double.