Palermo is a beautiful city with a rich history and culture. Here's an ideal itinerary for 4 days in Palermo:

Day 1:

• Start your day with a visit to the Palermo Cathedral, a stunning example of Norman architecture.
• Next, head to the nearby Quattro Canti, a beautiful square that marks the intersection of Palermo's four historic districts.
• From there, take a stroll through the colorful and bustling Ballarò Market, where you can sample local street food and pick up souvenirs.
• In the afternoon, visit the Palazzo dei Normanni, a magnificent palace that has served as the seat of Sicilian government for centuries.
• End your day with a visit to the Teatro Massimo, one of the largest opera houses in Europe.

Day 2:

• Start your day with a visit to the Capuchin Catacombs, a macabre but fascinating collection of mummified bodies.
• Next, head to the nearby Orto Botanico di Palermo, a beautiful botanical garden that's perfect for a leisurely stroll.
• In the afternoon, visit the Museo Archeologico Regionale, which houses a vast collection of ancient artifacts from across Sicily.
• End your day with a visit to the Piazza Pretoria, a beautiful square with a stunning fountain and plenty of cafes and restaurants.

Day 3:

• Start your day with a visit to the Monreale Cathedral, a stunning example of Norman architecture located just outside of Palermo.
• Next, head to the nearby La Zisa, a beautiful Arab-Norman castle that's now a museum.
• In the afternoon, visit the Palazzo Abatellis, a beautiful Gothic palace that houses a collection of medieval and Renaissance art.
• End your day with a visit to the Foro Italico, a beautiful waterfront park that's perfect for a sunset stroll.

Day 4:

• Start your day with a visit to the Catacombe dei Cappuccini, another collection of mummified bodies that's even more macabre than the Capuchin Catacombs.
• Next, head to the nearby Mercato del Capo, another bustling market where you can sample local street food and pick up souvenirs.
• In the afternoon, visit the Museo Internazionale delle Marionette, a museum dedicated to Sicilian puppetry.
• End your day with a visit to the Castello della Zisa, another beautiful Arab-Norman castle that's now a museum.

Of course, this itinerary is just a starting point - there's so much to see and do in Palermo that you could easily spend weeks exploring the city and its surroundings. But I hope this gives you a good idea of what to expect and helps you plan your trip!