Palermo is a beautiful city with a rich history and culture. Here's an ideal itinerary for 3 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, and catch a performance if possible.

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 Piazza Pretoria, a beautiful square with a stunning fountain and surrounded by historic buildings.
• From there, visit the nearby Church of San Cataldo, a beautiful example of Arab-Norman architecture.
• In the afternoon, take a stroll through the beautiful Botanical Gardens of Palermo, which feature a wide variety of plants and trees from around the world.
• End your day with a visit to the Palermo Art Gallery, which houses an impressive collection of paintings and sculptures from the 16th to the 20th century.

Day 3:

• Start your day with a visit to the Zisa Castle, a beautiful example of Arab-Norman architecture that was once a summer residence for Sicilian kings.
• Next, head to the nearby Villa Malfitano, a beautiful historic villa with stunning gardens and a collection of art and antiques.
• From there, visit the nearby Orto Botanico di Palermo, a beautiful botanical garden that is home to a wide variety of plants and trees.
• In the afternoon, take a stroll through the historic Kalsa district, which is filled with beautiful buildings, churches, and museums.
• End your day with a visit to the Palermo Archaeological Museum, which houses an impressive collection of artifacts from ancient Sicily.

Of course, this itinerary is just a starting point - there are many other wonderful things to see and do in Palermo, so feel free to customize it to your interests and preferences. Enjoy your trip!