The Castello Sofrzesco, an easy walk from the Duomo, was largely rebuilt during the 19th-century, so there is little left of the original medieval structure, but it now hosts an array of exhibitions. All of these can be visited for as little as three euros per person, under-18s get in free.
Piazza Castello, subway line 1 (red), Cairoli stop; www.milanocastello.it/ita/home.html
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