Milan’s Civic Aquarium brings a bit of sea to the middle of the city. It’s a magical place for kids, who can see fish with their own eyes and go through an underwater tunnel imagining that they are fish too or adventurous explorers. 
www.acquariocivicomilano.eu

Sforzinda is a permanent recreation and meeting space, designed for kids from 4 to 11, in the Castle’s basement. It offers various activities centring on knowledge of the Castle Sforzesco, to educate children in beauty and art. Castle visits for kids are structured around fairytales, games and shows. 
https://www.milanocastello.it/it

Milan’s Archaeology Museum is in two places: the Greek, Etruscan, Roman, Barbarian and Gandhara sections are in the monastery of the church of San Maurizio at Monastero Maggiore, while the prehistoric, ancient Egypt and epigraphy sections are in the Castello Sforzesco. Guided tours of the museum and visits to monuments in the city are provided for families and school groups by Aster, an educational Company. 
http://www.museoarcheologicomilano.it/wps/portal/luogo/museoarcheologico

MUBA is a centre of culture and creativity for children and their families. Located in the evocative setting of the Rotonda della Besana, it offers visitors a rich calendar of events: three large scale annual exhibitions and numerous projects in tandem with major events in Milan, such as the Furniture Show and Book City. 
www.muba.it

If you’re over 3, you can go aboard the submarine TOTI for an “immersion” in the fascinating undersea world, complete with periscope, sonar and watertight compartments. The vessel is in the “Leonardo da Vinci” National Science and Technology Museum. 
www.museoscienza.org/toti

This is a melting pot of cartoons and cinema, the worlds of animated drawings and popular literature, music and games. 
http://www.museowow.it/wow/it