A week end of friends, museums, Libertines concert, and some shopping, definitely.
You can flight to Milan from Luxembourg Findel airport directly. With Easyjet, with some advance, you can manage to get favorable prices even for Friday – Monday flights.
Easyjet flight is landing at Malpensa Airport Terminal 2. From there, you can take a free shuttle to Terminal 1 (10 minutes) and from there getting a train directly to Milan Central Station or Cadorna Station. The ride is taking 40 minutes and costs around 10 euros.
From Terminal 2, you can also take a direct bus for a cheaper price, but the motorway could get pretty busy during pick hours, so you should take in consideration a longer journey.
Just couple of address to recommend in Milan:
Maison Borella hotel, Navigli area. Intimate and Luxury. Outstanding service.
Zen Restaurant, Corso Italia area. Great sushi. Service a bit messy. Really fair price (Sushi Boat below around 15 euro per person)
Mercato Metropolitano, Porta Genova area. It a an open-air market where you have ton of street food trucks . From fish and chips to oysters, from Sicilian food to wine stand, from cocktail area to Burgers. You have only to choose!