I spent a day in Milan a few years ago and visited the Duomo Di Milano and the Parco Sempione with lunch at a wonderfully Italian mozzarella bar called Obikà - Milano Duomo which is right nearby in a department store overlooking the cathedral. It's right in the centre and a very pretty area of the city. I'm sure I missed a lot of amazing attractions but, like you, I didn't have the time so just wanted to enjoy myself a little! Hopefully some other people can suggest more places of interest for you :) 

We ended an eight day tour of Italy at the Crowne Plaza Milan - Malpensa Airport an airport hotel which was about an hour from Milan. We stayed an extra day in order to see a bit of Milan. The question was how to get from this hotel to Milan affordably. There was a free shuttle from the hotel, plus the nearby Holiday Inn Express to the airport. Malpensa AirportFrom the airport we could take a train from terminal 1 to Cadorna (Stz Nord) for about 11 Euros as recommended by the hotel clerk and which we should have done. or an express bus which runs every 20 minutes from either terminal to Milano Centrale Railway Station about one hour, 16 Euros round trip per person (10 Euros one way). Milan Centrael is a long walk to the area we wanted to be. We could have taken the Metro line 3. which we did on our return to Milano Central for our return trip to our hotel. Milano N. Cadorna would have been a better choice as far as proximity to the Duomo Di Milano I believe a taxi would have cost us about 50 or more Euros one way.