Begin in Milan with Leonardo and the marble spires of the Duomo, then travel east to Verona and Venice. Two nights in each city leave a full day for a main visit and evenings that are worth enjoying in their own right. Saffron risotto in Milan, an Adige walk in Verona and cicchetti beside a Venetian canal give the week a flavour beyond its famous monuments.
Verona makes a lovely middle stop. Its Arena links Roman spectacle with an opera tradition that began in 1913; Castelvecchio brings medieval history and Carlo Scarpa’s museum design into the same visit. Venice changes the setting again, with the layers of Saint Mark’s façade and streets that lead towards the water.
Use Milano Centrale, Verona Porta Nuova and Venezia Santa Lucia for the train sequence. Flights into Milan and out of Venice suit the eastbound journey, with six nights across seven days including arrival and departure. Spend the afternoons after each train getting to know the next city, then give its main collection or monument the following day.