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If you’re of a certain age, and of a certain level of cultural immaturity, it’s hard not to gaze upon Los Angeles City Hall and have two distinct reactions.

The first is to hear the opening notes of the theme from “Dragnet:” dum DA dum dum. The bullet-shaped, 32-story tower appeared in every episode. “I work here,” said Sgt. Joe Friday. “I carry a badge.”

The second reaction is mild astonishment that the 80-year-old landmark is still here. I, like a lot of people, assumed it had been shuttered long ago and replaced with something shiny and postmodern.

For years I’d thought the same thing about the neighborhood over which it presides, Los Angeles’ once-vibrant downtown. Abandoned in the decades after World War II in what Angelenos call the Great Freeway Diaspora, downtown had become a skid row hemmed in by sterile office towers.

But this is rapidly changing. The opening of the Frank Gehry-designed Walt Disney Concert Hall 3 1/2 years ago put an exclamation point on downtown’s comeback, which has been a decade in the making. It’s still very much a work in progress — and will be for years to come — but fashionable restaurants and clubs are opening where you once found only pawn shops, and young professionals are returning as long-vacant Beaux-Arts and Renaissance Revival buildings are scrubbed clean and converted into loft apartments.

On a recent visit it was the old, rather than the new, that interested me. On Broadway, with its almost unbroken stretch of buildings from the 1920s and early ’30s, it takes only a little imagination to transport yourself back to the Los Angeles of Raymond Chandler, “Chinatown” and fedoras. In a city that adopts a new look about as often as Angelina Jolie adopts children, it’s remarkable how many vintage restaurants and theaters survive.

The carrot-and-raisin salads still slide under the sneeze guards at Clifton’s Cafeteria, as they have since it opened in 1935. Possibly the first theme restaurant on the West Coast — its “American wonderland” style is an obvious inspiration for Disneyland — it’s virtually unchanged over the years. Patterned after the Brookdale Lodge in the Santa Cruz Mountains, it’s got a 20-foot waterfall, a babbling brook, fake redwood trees, stuffed raccoons, moose heads and wagon-wheel chandeliers.

Upstairs there’s a little chapel where you can hear a scratchy recorded message of inspiration. I thought it pretty hokey until I learned its origin: Founder Clifford Clinton installed it to buck up the spirits of his customers during the depth of the Great Depression, when he fed so many down-on-their-luck Angelenos for free he nearly went bankrupt.

In the 1930s, Broadway had the largest concentration of grand and gilded movie palaces in America — combined, they could seat 17,000 people — and many of these Art Deco and Beaux Art treasures are still in pristine condition.

The Orpheum’s stage has seen everyone from burlesque queen Sally Rand to a young Judy Garland — who was still going by Frances Gumm at the time — and in recent years has been the venue for “Hollywood week” on “American Idol.”

These days the theaters are mostly reserved for private events, but once a year a few of them open to the public for “Last Remaining Seats,” a festival of classic films with special guests. This year’s festival runs through June 27.

At the far end of downtown, near the revived Union Station, is my favorite dining joint in the neighborhood: Philippe, which claims to have invented the French dip sandwich.

It’s been in operation since 1908 (since 1951 at its present location), and still exudes the flavor of a bygone era, with ceiling fans, sawdust on the floor and long tables that diners share with strangers. A cup of coffee costs 9 cents (a dime with tax).

At the counter you order your sandwich made with beef, ham, turkey, pork or lamb — either single or double dipped — and accompanied by pink beans, homemade potato or macaroni salad, pickled eggs or pigs’ feet.

In a city not known for its bonhomie, there’s a rare feeling of camaraderie and fellowship as diners tuck their ties into their shirts and pass each other napkins to dab their chins.

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IF YOU GO

GETTING THERE

Downtown is probably the only part of Los Angeles where a car is not only unnecessary but likely an impediment. From Los Angeles International Airport, take the FlyAway bus ($3) directly to Union Station, where the Red Line subway ($1.25 a ride) can take you within a couple of blocks of any point downtown.

WHERE TO STAY

Los Angeles Athletic Club, 431 W. 7th St.; 213-625-2211; www.laac.com. At the city’s oldest private club, where I stayed, standard rooms for non-members are $161, including a good buffet breakfast in the Grill Room and use of the athletic facilities.

Hilton Checkers Hotel, 535 S. Grand Ave.; 213-624-0000; www.hiltoncheckers.com. Boutique-style hotel, gutted and rebuilt in 1989; modern, spacious rooms have 27-inch flat-screen TVs, CD players, granite-top desks and ergonomic desk chairs. Weekends from $199.

Figueroa Hotel, 939 S. Figueroa St.; 800-421-9092 or 213-627-8971; www.figueroahotel.com. Near Staples Center. Looks like a cross between a Mexican cantina and Rick’s Cafe; attracts young, hipster crowd. From $134.

WHERE TO EAT

Clifton’s Cafeteria, 648 S. Broadway; 213-627-1673; www.cliftons cafeteria.com. Entrees $2.75-$7.99.

Philippe, 1001 N. Alameda St.; 213-628-3781; www.philippes.com. French dip sandwiches, $5.15. Remarkably good wine list for the venue.

WHAT TO DO

Last Remaining Seats, 213-623-2489; www.laconservancy.org/ remaining/index.php4. Classic film series in classic film palaces, May 23-June 27. $15. Note: This year films will play in downtown theaters, Hollywood and Glendale.

Walking tours, 213-623-2489; www.laconservancy.org/tours. Los Angeles Conservancy’s walking tours include one visiting many of Broadway’s historic theaters. (This tour is on hiatus; check Web site for updates.) Others focus on Little Tokyo, Union Station and other aspects of downtown. $10.

INFORMATION

Los Angeles Convention and Visitors Bureau: 800-228-2452; www.seemyla.com.

— J.F.