Museums should mostly be open (see the hours for the Brera, here:
http://pinacotecabrera.org/en/visit/hours/ ). Among the many things to see are the city center (Duomo, Galleria VE, Fashion "Quadrilateral") the various big museums (e.g., Brera and Castello Sforzesco) and some of the house museums (I have enjoyed greatly Poldi-Pezzoli, Bagatti Valsecchi and Necchi Campiglio, more here:
https://casemuseo.it/en/ ).
Not sure how many restaurants will be open in midAugust but there should be some worth visiting. Plus various churches and other stuff you may be interested in (e.g., museums dedicated to Leonardo or twentieth century art [Novecento in Italian] or many others).