The velvet rope stretches in front of a doorway to the Ace Hotel, a hip hot spot in burgeoning downtown Los Angeles.

The doorman doesn’t look intimidating. Actually, the gatekeeper is a woman. A petite woman at that.

“Did you RSVP?” she asks when I approach.

“No,” I demur. “I didn’t know you had to.”

She gives me the once-over, asks if I’m alone (I nod) and she waves me in.

To the elevator, that is. With its checkerboard floor and dark wainscoting, it hardly screams like a vehicle to hipster heaven. But it takes you to the revered rooftop, the right spot if you’re a rock star, A-list scenemaker or Hollywood wannabe. Or just a voyeur.

The crowd makes the point: Nowadays, it’s fashionable to be in the revivified downtown L.A. The once seedy home to the homeless keeps turning trendier and becoming more popular, offering the right combination of retro cool and nouveau artsy — from the glitzy brand-new Broad modern-art museum to 100-year-old dive bars.

The Ace Hotel, 929 S. Broadway, may not be the epicenter of downtown L.A., but the rooftop is a place to see and be seen, especially for anyone who is under 35 or wants to be with someone who is.

A view from the top takes in the “Jesus Saves” red neon sign, a beacon in downtown L.A. since 1990, when the Ace building was a church. Off in the horizon, the Eastern Columbia Building shows off its big-as-Big Ben clock. Above, the latticed gothic tower atop the Ace Hotel looms.

Adding to the scene, people warm up by a large fireplace, dance to the DJ du jour or stick their feet in the pool (or hot tub).

Opened in early 2014, the Ace, part of an exclusive chain of boutique hotels, operates in the 13-story, 88-year-old restored United Artists Building. It has pricey rooms and a well-reviewed restaurant (L.A. Chapter) where a twenty-something waiter in a jean jacket can talk knowledgeably about the Velvet Underground.

But the real jewel is the Theatre at the Ace Hotel, a flagship of the United Artists studio founded by Mary Pickford, Douglas Fairbanks and Charlie Chaplin.

The ornate interior of the United Artists Theatre was designed by Anthony B. Heinsbergen. With its vaulted ceilings, fresco mural paintings, plaster castings, stone spires and chandeliers, it reflects Pickford’s love of castles and cathedrals in Spain, where she and Fairbanks romanced.

The 1,600-seat venue is used for special events (Gloria Steinem interviewed by Melissa McCarthy), movie screenings and regular concerts by the likes of Elvis Costello, the Dave Rawlings Machine and Loreena Mc­Kennitt.

Indeed, the Ace is the place.

• • •

With a vibe that might suggest New York City in the 1970s, once downtrodden downtown L.A. (shorthand: DTLA) is now a mix of gentrification, hipster renovations and showy new buildings that house museums and music halls.

And then there’s the Last Bookstore, 453 S. Spring St., a funky maze of books, vinyl albums, art and quirkiness that must have been designed by the bohemian nephew of Doc Brown from “Back to the Future.” There are more than 250,000 titles (new and used) in this sprawling, 10-year-old shop in the Spring Arts Tower, which once housed a bank.

The first floor features a stage for readings and music performances, hopelessly lived-in leather chairs and shelf after shelf of books and LPs. But let’s be honest, the real attraction is the second floor.

Crooked bookshelves (they’re art installations) greet you. Then enter the labyrinth that takes you through fantasy, sci-fi, mysteries and thrillers. That’s the first room. Watch for the curved bookshelves (more art installations) and other artful ways of displaying books. Continue on to the $1-a-book room and the area where books are sorted by the color of their spines, rather than genre, topic or author. Did I mention the crime, law and horror books located in an old bank vault?

“It’s the energy that brought us all here,” said artist David Lovejoy, who has a studio in the Last Bookstore.

Besides books, the second floor houses art galleries, a yarn shop and artist studios, including one featuring a “jangleodeon piano,” a jury-rigged upright featuring bells and various found percussive devices that promise “musicality plus added noise.” Somehow that description fits the irresistible hodgepodge that is the Last Bookstore.

• • •

The newest jewel in DTLA opened in September — the Broad, 221 S. Grand Av. It’s a $140 million contemporary art museum featuring the 2,000-piece private collection of Edythe and Eli Broad (rhymes with road), a billionaire who is the only person to create two Fortune 500 companies in different industries (homebuilding and financial services).

Admission is free to this bold origami box of a building with all kinds of odd angles. (Reservations are recommended; parking cost me $22 for three hours.) Gallery space — 50,000 square feet of it — covers two floors. (There is also 21,000 square feet of storage space on-site for the Broad’s massive collection.) Figure two hours to see everything that’s on display.

Take the escalator to the third floor and work your way down. Check out Jeff Koons’ oversized “Tulips,” and the Andy Warhol room with images of Campbell’s soup cans, Jackie Kennedy and Elvis. Jasper Johns’ “Flag” hangs here, as do works by Roy Lichtenstein, Keith Haring, Jean-Michel Basquiat, Kara Walker and others. Walk under Robert Therrien’s “Under the Table,” a giant table and chairs.

Work your way to the Broad’s first floor for pieces by Robert Longo, Goshka Macuga and Mark Grotjahn, whose “Dancing Black Butterflies” series occupies two walls.

Don’t miss the mesmerizing 2012 video installation by Iceland’s Ragnar Kjartansson called “The Visitors,” in which he filmed and recorded musicians in various rooms in an upstate New York house, all playing a piece of music (depicted on nine screens) and eventually ending up in the same room.

This shiny, polished place is as self-consciously far-out as the dusty, offbeat Last Bookstore is lovably eccentric. Somehow both feel sooo L.A.

The main interior architectural feature of the cavelike Broad is a honeycomb of skylights.

This brand-new art museum stands in curious contrast to its across-the-street neighbor, the Walt Disney Concert Hall, the Frank Gehry structure that is stunning for its acoustics, architecture and massive pipe organ.

Like the Gehry-designed Weisman Art Museum at the University of Minnesota, the 12-year-old Disney, 111 S. Grand Av., is a stainless-steel-wrapped marvel, all weird angles and shapes.

The interior is as striking as the exterior. Take a self-guided or guided tour through the curvy staircases and walls, and notice the floral-patterned rug requested by Lillian Disney (Walt’s widow) because she loved flowers and gardens.

There are also inviting outdoor spaces, including an amphitheater for music and gardens for picnics. The L.A. Philharmonic, under the baton of Gustavo Dudamel, performs in this pristine hall, which also presents pop concerts by the likes of Gladys Knight and Kristin Chenoweth.

Unlike the food-free Broad, the Disney has a cafe and a high-end restaurant, Patina. Disney never misses a marketing opportunity. But you knew that.

• • •

If the Broad and Disney Music Hall represent the new architectural landmarks of downtown L.A., the Bradbury Building, 304 S. Broadway, stands for the old.

Built in 1893 after being commissioned by gold-mining millionaire Lewis L. Bradbury and restored in 1991, this five-story brown-brick building hardly looks distinguished from the outside. But the interior is a jaw-dropping feast of Italian Renaissance Revival, complete with ornamental cast iron, Italian marble, Mexican tile, decorative terra cotta and caged elevators in a narrow, cathedral-like center court capped by a mammoth skylight.

The Bradbury has five floors of offices, including the Los Angeles Police Department’s Internal Affairs Division. There are a few retail shops on the first floor, such as Ross Cutlery, where O.J. Simpson bought a knife that figured in his notorious murder trial.

With all its remarkable architectural features, the Bradbury has been used in dozens of movies, including “D.O.A.” (1950), “Chinatown” (1974), “Blade Runner” (1982) and “The Artist” (2011). Among the TV shows filmed there are “77 Sunset Strip,” “The Outer Limits” and — go figure — “CSI: NY.” The interior has been featured in music videos by Janet Jackson, the Pointer Sisters and Heart.

Despite its fame, the Bradbury can be as quiet as a cathedral — and just as peaceful. Sit on a pew, er, wooden bench next to a life-size statue of Charlie Chaplin. You’ll feel like a character in a silent movie.

• • •

No true maroon-blooded Minnesotan can go to downtown L.A. without visiting the Golden Gopher Bar, 417 W. 8th St. Founded in 1905, it boasts the city’s longest-running liquor license and kept pouring during Prohibition with near-beer and medicinal alcohol, manager Francois Houlard said.

Where did the name come from? “My understanding is that one of the first owners, he was from Minnesota and went to the University of Minnesota,” Houlard explained.

The Golden Gopher isn’t a college bar. It’s more of a dimly lit neighborhood joint for hipsters, a place that’s retro cool and overrun with rodents. Little golden statues are part of the light fixtures on the tables and walls — the plumpest golden gophers you’ve ever seen.

To add to the ambience, there’s gold felt on the pool table. (A recent upgrade, Houlard said.) The jukebox is stuffed with golden-oldie CDs including the Who’s “Pinball Wizard” and David Bowie’s “Suffragette City.” Adding to the old-school vibe, there are video games such as “Pac-Man” and “Space Invaders.”

“We like dive bars,” said Gopher-goer Phil Zubia, 30, a graphic designer from Monrovia, Calif. “This place has a cool atmosphere.”

“There’s no cover charge. In L.A., that’s really good,” noted Adel Diaz, 31. “And no line.”

Besides being old and filled with artificial rodents, the Golden Gopher has another thing that sets it apart — an off-sale license. Yes, you can buy a to-go bottle for your after-party. Can I get a “rah, rah, rah for Ski-U-Mah”?