I'd stay near Central Train Station. You probably find some hotel slightly higher than €100.
From MXP by airport express train direct to Central Station.
I had stayed at the Four Points by Sheraton last year. Excellent hotel. Took me less than 10 minute walk with luggage from the station. Few restaurants nearby.
You can go almost anywhere in Italy by train. Hence the train station hotel is ideal.
Take the Metro to Duomo.