Galleria Vittorio Emanuele
Walking from the Piazza Duomo to the Piazza della Scala you walk through this beautiful glass roofed area with expensive shops, cafes and restaurants. Treat yourself to a cup of coffee and watch the people walking by. The floors are decorated with mosaics of the signs of the zodiac (touch the genitals of Taurus with your heel for good luck).
Accessible from the Piazza della Scala and Piazza Duomo.
Piazza della Scala
On one site of the square there is La Scala (famous opera house) and on the other site the Palazzo Marino (now the city hall). In the middle stands a statue of Leonardo da Vinci surrounded by his pupils. One of the entrances of the Galleria Vittorio Emanuele is accessible from here.
Teatro della Scala
This is one of the most famous opera houses of the world. For every opera singer it's a dream to perform here. During my visit the theatre was still under major restorations. It opens again in 2005. Till then the performances take place in the Teatro degli Archimboldi.
Address: Piazza della Scala http://www.teatroallascala.org
Behind one of the passages of the Castello Sforzesco you'll find the Sempione Park. It's a nice place for a picnic. I especially liked the iron bridge with the mermaids (see the picture).