Milan may be losing to Rome, Venice and Florence, when it comes to the number of tourists visiting Italy annually, but it is hard to contest the notion that the trip to the northern fashion capital would be worth your while. If you want to explore Italy in more detail, than Milan is a must-see place on your list. Advice on the best time to go to Milan is no different from advice for most other large European cities and destinations.
The rule of thumb, when it comes to visiting Europe, is to remember that in summer travel and accommodation are more expensive, the weather is hotter, and many places may end up closed in August. In autumn, especially at the end of September and in October, crowds recede, prices stabilize, and the weather in general is still nice enough for sightseeing, if not for sun bathing. Depending on the destination, wintertime may appropriate for a visit as well, but bear in mind the inevitable Christmas rush and holiday price hikes.
All of the above applies to Milan, with three important additions: Milan Fashion Week in March, Milan Fashion Week in early October, Milan Designer Week in mid-April. The weather of course could not care less about haute couture, and it usually behaves during these important events. The culprit about visiting Milan at this time is accommodation prices that skyrocket like there is no tomorrow. To secure an apartment (the main advantages of renting an apartment in Milan are listed here) or a decent hotel room within city limits for a reasonable price, you need to book several months in advance. Closer to the event, especially the Milan Designer Week, you will not find anything for less than a 500 euros per night. So, unless you work in the fashion industry or have been planning to visit Milan during Fashion Week specifically, postpone your trip. The spirit of fashion lingers in Milan year-round, after all, and there is no reason to pay arm and leg to feel the part of it for a few days.