When visiting Milan, there are several activities and attractions to consider, including:

1. Visit the Duomo: The Duomo di Milano Cathedral is a magnificent Gothic cathedral and the citys most important landmark. Visitors can explore the interior and also visit the top to see Milans ever-changing skyline.

2. Marvel at The Last Supper: The Santa Maria delle Grazie convent is home to Leonardo da Vinci’s mural “The Last Supper,” a historic and cultural activity not to be missed.

3. Explore the Navigli District: Sink some canalside drinks and enjoy the vibrant atmosphere of this district.

4. Teatro Alla Scala: Visit this renowned opera house and museum.

5. Pinacoteca di Brera: Explore this public gallery showcasing Italian paintings from the 13th to the 20th century.

6. Science & Technology Leonardo da Vinci Museum: Another popular museum in Milan worth visiting.

7. Day Trips: Consider taking a day trip to Lake Como or exploring nearby beaches for a change of scenery.

8. Shopping: Milan is known as the fashion and design capital of Italy, offering a wide range of shopping options, including the Quadrilatero della Moda.

9. Cultural and Culinary Experiences: Try risotto alla Milanese, take a Milan food walking tour, and explore the citys vibrant art and design scene.

10. Poldi Pezzoli Museum: Stand in the Golden Room of this museum, often overlooked but worth a visit.

Remember to check the dress code in advance when visiting certain attractions, and consider the logistics of getting around Milan to make the most of your time in the city.