Here's an ideal itinerary for 7 days in Milan:

Day 1: Arrival and Exploration

• Arrive in Milan and check into your hotel
• Take a stroll around the city center to get a feel for the city
• Visit the iconic Duomo di Milano, one of the largest cathedrals in the world
• Explore the Galleria Vittorio Emanuele II, a stunning shopping arcade with high-end boutiques and restaurants

Day 2: Art and Culture

• Start your day at the Pinacoteca di Brera, a museum filled with Italian Renaissance art
• Visit the Castello Sforzesco, a medieval castle that now houses several museums and art collections
• Take a walk through the trendy Navigli district, known for its canals and vibrant nightlife

Day 3: Day Trip to Lake Como

• Take a day trip to Lake Como, one of the most beautiful lakes in Italy
• Enjoy a boat ride on the lake and take in the stunning views of the surrounding mountains and villas
• Visit the charming town of Bellagio, known for its picturesque streets and gardens

Day 4: Fashion and Shopping

• Spend the day exploring Milan's fashion scene
• Visit the Quadrilatero della Moda, a neighborhood filled with designer boutiques and luxury stores
• Check out the Armani Silos, a museum dedicated to the work of fashion designer Giorgio Armani

Day 5: Food and Wine

• Take a food and wine tour of Milan
• Visit local markets and taste traditional Italian dishes like risotto alla milanese and ossobuco
• Sample some of the region's famous wines, such as Barolo and Chianti

Day 6: Leonardo da Vinci and Science

• Visit the Leonardo da Vinci Museum, which showcases the artist's inventions and machines
• Explore the Museo Nazionale della Scienza e della Tecnologia, a museum dedicated to science and technology
• Take a walk through the Parco Sempione, a large park in the heart of Milan

Day 7: Relaxation and Departure

• Spend your last day in Milan relaxing and taking in the city at your own pace
• Visit one of Milan's many parks or gardens, such as the Giardini Pubblici Indro Montanelli
• Depart from Milan and head home, or continue your travels elsewhere in Italy.