Having lived in Milan while Design Hovie Studios' main studio was located there, many people ask me what they should do for their day or so in the city. (seems most people only are flying in or out and never stay more than a day). In any event here is my one day in Milan itinerary.
Take the Metro or bus to the San Babila. Check out the great, old San Babila church and then start walking down Corso Vittorio Emanuele toward the Duomo and soak in all the great shops along the way. Explore the Duomo in all it grandeur and then enjoy people watching on its steps while gazing out on the piazza. Next check out the Galleria adjacent to the piazza and then head back to the piazza and continue down Via Orefici to Via Dante, again soaking in the shops, and continue on to the Castle. The Castle has a nice museum and amazing grounds. All of this should take up a good portion of your day and, depending on how much you've shopped, could cost next to nothing.
After returning to your room for a brief nap. Head out for aperitivo (drinks and appetizers) around 6ish in the Naviglio district. It's full of lot's of great bars and restaurants and night life. Grab dinner there around 9ish and then possibly take in a club around 11-12ish. Note that the locals most likely won't be in the clubs on Friday, Saturday or Sunday as that's when the Milanese escape to the countryside.
Of course this is but a taste of Milan but for one day, I think this could give you a great feel for the city.