Milan is a city with two faces. On the surface it looks grittily industrial, yet it also has romance, if you know where to look. Glimpsed beyond its imposing grey stone facades are elegant courtyards and leafy gardens; its medieval streets are narrow and cobbled, but that doesn't stop 21st-century traffic racing down them at breakneck speed, past ancient, benignly neglected monuments.I've got to know Milan intimately as a visitor to the annual Salone de Mobile design fair, held every April, when people from all over the world flock to the city. Over the years, I've been thrilled by its passion for style and culture something that goes all the way back to the Renaissance, when Leonardo da Vinci came here to paint for the ruling Sforza dynasty.Maze-like and compact, Milan is made for walking. Take a good map and you can see most of these memorable places on foot, or hop on the super-fast Metro as need be.

Orto Botanico di Brera

The Brera district is the heart of Milan, but few tourists know about this 18th-century botanic garden, hidden behind the Pinacoteca di Brera gallery and art school. Walk to the back of the building and turn right; as the sound of sculpture students wielding chisels fades, you'll find a tranquil space filled with rare plants and tumbling wisteria.

Villa Necchi Campiglio

As a perfectly preserved example of 1930s modernism, it's no wonder this house was chosen as the backdrop for Luca Guadagnino's film I Am Love, in which Tilda Swinton plays a melancholy aristocrat. The sitting room decorated in watery greens, filled with Art Deco treasures and surrounded by views of trees, is the stuff of dreams.

Galleria Rossana Orlandi

Fashion lovers head to the 10 Corso Como concept store; this is its interiors equivalent, housed in an old tie factory on the city's west side. Scrapwood tables by Dutchman Piet Hein Eek mingle with fabric vases by Spanish artist Nacho Carbonell, while other outlandish pieces pop up between the shrubs in the courtyard caf. Linger awhile and you may spot Orlandi herself, lavishly bespectacled and chic as only the Milanese can be.

Fioraio Bianchi

Spend a morning rambling round Milan's answer to Central Park, the Parco Sempione, before walking a few streets east to this lovely caf. Its artfully distressed walls are contrasted with modern floral arrangements, all of which are for sale: contemplate your choice as you enjoy the superb coffee and flower-adorned desserts.

Fondazione Prada

Miuccia Prada commissioned architect Rem Koolhaas to turn an old distillery on the southern reaches of the city into this contemporary art gallery; it's worth visiting for the exterior alone, partly clad in gold leaf. Don't miss the caf, Bar Luce, designed by film director Wes Anderson. The cakes are iced in pink and green to match the retro interior.

Words by Amy Bradford

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