Neoclassical Milan
A few good options for Milan are Casa Baglioni, Palazzo Parigi, Mandarin Santa Sofia, Roommate Giulia , Park Hyatt Hotel, + I just found one I'd love to try, Foresteria. a small local hotel that has nice simple rooms and character. I heard the Carlton is good, now under the Rosewood umbrella..
Puntarelle
A typical roman salad with bitter greens and anchovy dressing. We had a fabulous easy lunch at Il Mercante, It's a beautiful space filled with art & portraits steps from the Duomo.
Duomo and Galleria Emanuele
Your first point of reference is the neoclassical Duomo and the Gallerias you find 'accanto' to it. From here you can decide to go towards Brera (walk behind La Scala) or towards the main high end shopping streets of Via Spiga, and Montenapolone.
visit the Rinascente (food on 7!) and the Novecento Museum. also try to see the Duomo from its top terrace. The floors are all marble and gorgeous.