Here's an ideal itinerary for 3 days in Milan:

Day 1:

• Start your day with a visit to the iconic Duomo di Milano, one of the largest cathedrals in the world. You can climb to the top of the cathedral for stunning views of the city.
• After that, head to Galleria Vittorio Emanuele II, one of the world's oldest shopping malls. It's a beautiful place to stroll around and admire the architecture.
• For lunch, try some authentic Italian pizza at Pizzeria Spontini or Luini Panzerotti.
• In the afternoon, visit the famous La Scala opera house and museum. You can take a guided tour to learn about its history and see the backstage area.
• End your day with a walk around the trendy Navigli district, known for its picturesque canals and lively nightlife.

Day 2:

• Start your day with a visit to the Pinacoteca di Brera art gallery, which houses an impressive collection of Italian Renaissance art.
• Next, head to Sforza Castle, a medieval fortress that now houses several museums and art collections.
• For lunch, try some traditional Milanese dishes like risotto alla milanese or ossobuco at Trattoria Milanese or Osteria del Treno.
• In the afternoon, visit the modern and contemporary art museum, Museo del Novecento, located in the heart of the city.
• End your day with a visit to the peaceful Parco Sempione, a large park with beautiful gardens and a lake.

Day 3:

• Start your day with a visit to the historic Biblioteca Ambrosiana, one of the oldest libraries in Europe. It houses a vast collection of manuscripts, paintings, and sculptures.
• Next, head to the trendy Brera district, known for its narrow streets, boutiques, and art galleries.
• For lunch, try some delicious street food at Mercato Metropolitano or the famous Luini Panzerotti.
• In the afternoon, visit the Leonardo da Vinci Museum, which showcases the inventions and works of the famous Italian artist and inventor.
• End your day with a visit to the beautiful Santa Maria delle Grazie church, home to Leonardo da Vinci's masterpiece, The Last Supper.

I hope this itinerary helps you plan your trip to Milan!