Milan has gained the stereotype of being a gray industrial city, focused on banking and business, however I would beg to differ that it is so much more. The booming industries here are hard not to notice between design, food, fashion, and finance. Women don't leave the house without their stillies, and more often than not, wear their sunglasses indoors. Milan radiates from Centro, which includes Duomo, Teatro Alla Scala, Quadrilatero D'Oro (Quad is the main fashion district), and the ancient paths of Vecchia Milano (Antiques/ Fashion/ Home). North of Scala is the artsy area of Brera (Fashion / Antiques) and Garibaldi. To the west is Genteel Magenta, Salone Del Mobile, Zona Tortona, and the Navigli Canals. To the East is buzzing Lambrate with Design Week and the Southeast is Porta Venezia, Porta Vittoria, and Porta Romana.
There is an Emirates direct flight from JFK to Malpensa that is my favorite way to fly into Milan. Most people try and avoid Malpensa airport since its about an hour away from Milan center by car (€90), but it's only 20 minutes on the Linate Train (€20). Taxis cannot be hailed in Milan (similar to Florence), so you have to catch one from the taxi stand or call for one (but keep in mind that they charge you from the time the call is placed). Uber works, but is expensive, so it's best to walk if you're in Centro, or take the metro if you are going outside of Centro. Similar to France, all shops are closed on Sundays, so it's best to explore a museum or gallery. There is a small cover charge at restaurants for tips that is already included in your bill, but it's always nice to leave a few extra euros.