Renzo Piano has a peculiarly zany grin for one of architecture’s greybeards, and he barely had to flash it at audiences at the Art Institute of Chicago on Saturday to have them erupting in hoots and hollers. “I love Chicago!” he said to cheers.

Piano was there to open his Modern Wing for the institute. It concludes a $300 million (£197 million) project that has been ten years in planning and four in construction, expanding the institute’s exhibition space by 35 per cent, taking it up to a roomy one million sq ft, making it the second-largest art museum in America after the Metropolitan in New York. It’s essentially a three-storey pavilion that extends from the rear of the institute’s late-19th-century Beaux Arts structure. Curtain walls of glass and steel enclose it, and a louvered canopy shades it from sunlight. The galleries are modestly proportioned and well lit. The arcade that forms the spine of the building is also graceful, with lighting fixtures suspended on a succession of steel arms. Visitors walk along corridors above it as if hoisted by sheer sweetness and light.

The wing adds another facet to Millennium Park, the 24.5 acre site at the centre of the city that is a marvel of variety and ingenuity, linking flowery pathways with public sculptures such as Anish Kapoor’s Cloud Gate and the fanciest bandstand in the world, Frank Gehry’s Pritzker Pavilion, which wears a headdress of billowing stainless steel ribbons and craves attention.

Chicago may be regarded as America’s second city yet the Art Institute is world-class. It incorporates a respected art school, and a museum whose collection runs from Ancient, South Asian and African art to Western design, decorative and fine art as far back as the late medieval period. It owns fistfuls of El Grecos and truckloads of Impressionism. Its trustees vow that Seurat’s A Sunday on La Grande Jatte shall never stray from its walls; nor will they relinquish Caillebotte’s biggest and best picture, Paris Street, Rainy Day.

Other highlights include Grant Wood’s American Gothic and Edward Hopper’s Nighthawks, and among the benchmarks now adorning the Modern Wing are Willem de Kooning’s Excavation and Henri Matisse’s Bathers by a River. The institute has taken heat from locals in the past for neglecting the city’s own artistic achievements, and you can see an effort to make amends in the extension. Mid American, a gaudy tribute to a fairground boxer, by the Pop-era Chicago painter Ed Paschke, opens the post-1960 galleries, and next to it sits a sculpture, Woman in Tub, by Jeff Koons, who studied at the institute’s art school.

Chicago’s cultural power has been fuelled not by the genius of its own artists but by the wealth of local industrial magnates eager to garland their city. Tom Pritzker is typical of them: the chairman of the Hyatt Hotel chain and the Marmon Group conglomerate and much else, he’s a lifelong Chicagoan. He heads the institute’s board and he funded Gehry’s pavilion. He’s also aware of the prestige that Chicago once had as a beacon for modern architecture. It was here that steel-frame construction was first perfected in the 1880s, making way for the first skyscrapers, and great names have put down influential buildings in the area, from Louis Sullivan to Frank Lloyd Wright and Mies van der Rohe.

A “second Chicago school” emerged in the 1960s when Fazlur Kahn introduced a new method of steel construction and gave birth to a new generation of tall buildings, including the Sears Tower, which, when it was topped out in 1973, was the tallest in the world. Sears remains America's top spot, and those with an iron stomach for heights may be pleased that the building is opening glass enclosed viewing platforms in June. They will extend 4.3 foot beyond the building on inch and a half glass so you can get the window-washers' view down from the 103rd storey.

But Chicago’s light has dimmed as a capital of architecture. Santiago Calatrava hopes to build a 150-storey twisting “spire”, which will supplant the Sears as North America’s tallest, but the proposed site remains a heap of rubble, and the recession may dampen his ambitions. Hence the city has put great hopes in Piano’s Modern Wing. It is serene, efficient, and yet it disappoints. It offers up no singular image: there is no bold gesture, no Tate Modern Turbine Hall that one might learn to love. In fact, the designs that Gehry and Piano have supplied for Chicago point to the twin dangers of “star-chitecture”: bombastic, signature gestures on the one hand, predictable products on the other.

It is telling that the most exciting building currently nearing completion on the Chicago skyline is the first skyscraper by Jeanne Gang, and the largest project yet awarded to an American firm headed by a woman. Called Acqua, it’s a skyscraper-as-waterfall, with curving balconies undulating in and out to evoke rocky outcrops, and areas of reflective glass to suggest cascading torrents. Sometimes, genuine innovation needs new blood.

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