Chicago's varied and enduring appeal

What I like about Chicago is that it wears so well. You read about the coming of yet another landmark skyscraper and wonder if Michigan Avenue will soon be listing toward the lake; but then you go back and find that the ''city of broad shoulders'' still remembers its past, still protects its aged buildings, and still roots for a team (the Cubs) that plays in an ivy-walled park without lights.

Even though it has three of the five tallest buildings in the United States and some of the country's flossiest downtown shopping atriums, Chicago will always be 1930 to me. Indeed the windows of Neiman-Marcus on Michigan Avenue were done in a 1930s motif when I passed by the other day, a salute to the movie ''The Natural,'' which has a number of Edward Hopperesque Chicago scenes.

I can't deny I am intrigued by the new buildings as well, for who does them better than Chicago? It was a lark one morning to zip up to the 94th floor of the Hancock Center and have the whole wraparound deck to myself, a shining view from lake to prairie. Only a few minutes later I was back to earth, directly across Michigan Avenue, enjoying the budding green calm of a church cloister, which seemed miles and not just yards removed from the Fifth Avenue of the Middle West.

Chicago is forever compared with New York. In an indelicate, put-down piece years ago, A. J. Liebling called it the Second City, but maybe now that Los Angeles has moved into the No. 2 position behind New York in population, Chicago can relax with its own identity. Surely it has its own rhythms and quirks, and the only one that gave me any difficulty this trip was the scheduling of its excellent and varied museums.

Setting out one Friday afternoon for the Institute of Art, my companion and I arrived at the twin lions in front at 3:40, only to learn that the museum would be closing in 50 minutes. Alas, 4:30 is a common closing hour in Chicago. We came back the next day to give the institute its due and, passing up a new show, headed straight for the second-floor European art treasures.

In a small, gemlike gallery, the Bartlett Memorial Collection residing there is getting more attention than usual these days. Dominating a wall opposite the entrance is the large and dazzling ''Sunday Afternoon on the Island of La Grande Jatte,'' by George Seurat. This and El Greco's ''Assumption of the Virgin'' are the principal masterpieces of the museum, but the Seurat is also the inspiration for the new Stephen Sondheim hit musical, ''Sunday in the Park with George.'' We stood around the large pointillist piece, with its parasols and bonnets and boats and scullers, simply happy to have a Saturday in the museum with George.

Forced to limit my museum hours by time and geography (Chicago's important institutions are spread for 10 miles along the lake), I took a stab at the Chicago Historical Society, on the edge of Lincoln Park, and came up with a winner. This time we arrived at 3:30, knowing there was only an hour to go, and ran through 150 years of city history in a lively, lovely blur. There is an ample exhibit of the 1873 Chicago fire which includes melted plates and charred ginger cookies that survived the storied blaze, along with a Norman Rockwell painting of Mrs. O'Leary's cow about to kick over the lantern. We did a quick cram course on Chicago architecture, the 1893 Columbian Exposition, and the 1933 World's Fair, and held on until the lights went out on a handsome exhibit of Chicago furniture down the years. This vast collection, which includes the rolltop desk of Marshall Field, the department-store baron, and a gaudy platformed, canopied bed from the old Palmer House hotel, will run until Aug. 31 .

Chicago is itself a museum of art and architecture, with a rich variety of public sculptures and historic buildings in full view. There are a number of guided tours to be taken, and among the most ambitious are those put on by the Chicago Architecture Foundation, whose headquarters is at the ArchiCenter, 330 South Dearborn.

Many of Chicago's hotels are reflective of the city's flavor and history, perhaps none more so than the Drake, an 11-story brick pile ideally cornered between the lake and Michigan Avenue. The dowager Drake had fallen on hard times , but a $12 million Hilton renovation since 1981 has brought back much of the old mood and appearance while instilling just enough high-tech convenience. I am a longtime lobby lounger, and the Palm Court was a happy refuge at all hours - reminiscent of the Palm Court in the Plaza in New York - but more comfy and inviting.

Another hotel that smacks of old Chicago is the Ambassador East. Its lasting fame is for the Pump Room, a landmark restaurant that has been gleamingly redecorated but still gives off the air of an old-fashioned Chicago supper club, which it was when Joan Fontaine, Helen Hayes, Frank Sinatra, and Joseph P. Kennedy (a one-time resident) were in the house and dining at table No. 1.

Two of Chicago's greatest assets, sometimes overlooked by the hurried visitor , are the parks and the lake. In what other metropolis can you find a limitless blue body like Lake Michigan lapping at the very edges, or a popular sandy beach like that at Oak Street only a short stroll from the main shops? Zoos are another Chicago blessing, which I learned from my seatmate, a biologist, on a Midway-Metrolink flight from the convenient Midway Airport to New York. She said I had missed something by not visiting Brookfield and Lincoln Park Zoos. But there will be other visits to the ''city of broad shoulders'' - and its surprising museum hours.