Worth a day trip but nothing more
Milan is worth a quick stop in; climbing up the Duamo is fun! However, if you are limited on time, or are picking a city to travel to for vacation, unless you are very much into shopping and fashion, I would pick elsewhere. If Italy is the county you want to visit, I suggest either Venice for a tranquil and beautiful holiday or Rome for the history and sightseeing.
Insider Tip:Buy the Milano sightseeing card if you are there for a couple of days, but dont forget to download uber for your free taxi ride. Try to take a trip to Lake Como if you can. There are numerous tours that will take you there from Milan, else there are direct trains if you want to do it on your own. If its a nice day, its worth taking the slow (2 hour) boat to the island of Bellagio. You won't regret it!