Moscow likes to bombard the people who live and travel here with its size, importance and power. Its icons command devotion. Its wide boulevards and dense buildings overpower the pedestrian. And no matter how many times I pass the picture-perfect onion domes of St. Basil’s, the spiraling, zigzagging, swirling gold-gleaming church towers never fail to humble. It’s a grand city — and a tacky city, crowded with crumbling Soviet-era apartment buildings and nouveau-riche glass towers. It’s status-obsessed — the shabby 40-year-old complex where I live has a Porsche dealership on the first floor and a Rolls-Royce showroom across the street. Prada reigns a few blocks away, and drunks sleep in my neighborhood park. At the same time, it’s resolutely dismissive of everyday life, with dreary storefronts and dark underground passageways where kiosks offer ordinary shoppers shoes, underwear, milk and bread.

It’s an amazing, intriguing and rewarding place — I never tire of urging friends to visit — and I thought I knew it pretty well, until I discovered another Moscow, nearly hidden somewhere between excess and deficiency, a very cool city with cutting-edge galleries, cafes and clubs, all informed by an urbane sensibility and designed on an intimate scale. Call it hip Moscow.

Moscow, hip? Hip, after all, speaks to the individual, the personal, the idiosyncratic, and it should involve some fun, a word that doesn’t even translate well into Russian. I’d lived here some years ago and returned last fall to report from The Post’s Moscow bureau. I thought I knew Moscow 2011, but it took visitors from Washington to help me discover hip Moscow. You know how it is — you can walk past the Smithsonian every day for years but never know that the Hope Diamond lies sparkling inside until a cousin comes to stay.

My friends Sue and Chris, who had both worked here in the 1990s, crammed in two days of sightseeing after coming to town for a conference a few weeks ago. They already knew the Kremlin and the well-established museums, and now they wanted to see the less familiar. They ended that Saturday astonished after visiting the bright white box of the Multimedia Art Museum, on one of Moscow’s oldest streets, Ostozhenka, where the wealthy lived in the 16th-century era of Ivan the Terrible.

The museum was started in 1996 as the Moscow House of Photography and reopened at the end of last year as the Multimedia Art Museum after a five-year renovation. Sue and Chris were struck by how many young Muscovites and Russian families filled the museum, and how it engaged its visitors, with friendly docents and lots of information offered clearly in English and Russian.

The Moscow museums they’d known in the past were presided over by legions of stern women who expected visitors to show reverence rather than enthusiasm. Schoolmarm-style guides ruled with pointers, and the art, made long before anyone had heard of the word multimedia, came in a frame.

“It was like something in New York,” Chris said, exclaiming over the new museum, surprised at what had managed to emerge between the mustiness of the past and the garishness of the first post-Soviet decade.

Both understated and powerful, the museum was the inspiration of Olga Sviblova, who was once famously described by a British journalist as the most beautiful woman in Moscow. In the early post-Soviet years, she developed an interest in contemporary art, which was not favored with government interest or support.

“It was a very complicated time in Russia,” she told me. “We had to think about the future, but it’s impossible to think about the future without understanding the past. At the same time, Russia had been a closed country, and we wanted to open it to the world.”

Sviblova saw photography as a means to that end, as an art form but also a historical document, an intriguing pursuit in a country where Soviet-era photographs were altered to fit changing views of reality, and history. Turned out she had a great eye, putting together an extensive collection and becoming a well-known creative force — she was the curator of the Russian pavilions at the Venice Biennale of Contemporary Art in 2007 and 2009.

She originally put the word “house” in the museum’s name because she wanted to impart the sense of an open house. “I didn’t want the public to be the enemy,” she said. “I wanted to create something fresh, new, looking to the future.” It’s open until 9 p.m. If you work, she says, you can’t go to a museum if it closes at 6.

With photography, and the building’s constructivist look, the gallery evokes the last time Moscow was truly hip — the 1920s, when the city was the capital of the avant-garde, with artists like Alexander Rodchenko, a photographer and graphic designer of enduring influence, at work.

The museum displays both the Russian and the international, with a series of photographs by Sergei Shestakov on display through May 29, documenting what Chernobyl looks like 25 years after the disaster. A photographic journey through the life of Mick Jagger has just been taken down. Through July 10, a variety of contemporary works from the Castello di Rivoli, a castle that’s home to contemporary art in Turin, Italy, will be seen. And — just for fun — there’s a nice collection of Russian 3-D postcards from the ’70s.

From the museum, it’s a short walk across the bridge behind the Cathedral of Christ the Savior to the former Red October Chocolate Factory, where Moscow has discovered the cool quotient of old brick and industrial spaces. The 19th-century warren of warehouses on Bolotny Island, in the middle of the Moscow River, teems with appealing galleries such as the Lumiere Brothers Photography Center, coffeehouses, restaurants — and the Strelka Institute for Media, Architecture and Design, where Rem Koolhaas is a visiting professor.

The institute, which some of the city’s wealthy oligarchs opened last year to train students who might someday help the city adapt tastefully to the future, also houses Bar Strelka, one of the hot places in town for dining and drinking. The restaurant starts with breakfast — granola and Greek-style yogurt gives you an idea of its direction — and later in the day segues into burgers (on brioche) and a variety of meat, fish and vegetarian main courses.

You can wander around for hours here — it’s an inviting place to walk in, which is unusual for Moscow, where most walking is for transportation, not enjoyment. Same for Winzavod, a former winery near the Kursky train station that has some big-name contemporary galleries, including Aidan, Guelman and Regina, on its 215,000-square-foot grounds. At Proun Gallery, which specializes in Russian avant-garde, I watched an engrossing video called “Incidence of Catastrophe” by American artist Gary Hill, who was inspired by the 1941 existential novel “Thomas the Obscure,” by Maurice Blanchot.

At the Australian Cara & Co., which calls itself a concept store selling intellectual fashion, you can drink coffee on the mezzanine and watch as the beautiful people below choose among $600 sunglasses and $500 Robert Clergerie footwear (some on sale, a helpful saleswoman told me). Across the way, Gallery Baboushka is more affordable, selling felt necklaces for $22 and passport covers for $10.

Things don’t really get going at Winzavod until afternoon, and the place has more energy on the weekends. If you have time midweek, go to the Garage Center for Contemporary Culture, where I have waited in line on the sidewalk to get in on weekends but prefer the quieter weekdays. The Garage is one of my favorite places in Moscow, a vast space designed in 1926 by Konstantin Melnikov, a constructivist architect who was making a bus garage, but a beautiful one, where the buses could swan in and out without having to back out.

Daria Zhukova, girlfriend of the fabulously wealthy oligarch Roman Abramovich, opened it as a cultural center in 2008, and I found myself spending a good part of a recent day there, and half the night, fortified by a marvelous blue cheese and pesto pizza from the up-to-the-minute Garage Cafe. (This in a town where slices of pork fat are more traditional.) The Garage was open all night that Saturday so that fans of Christian Marclay’s video “The Clock” could indulge their addiction for 24 hours.

Alas, “The Clock” has moved on, but the time it spent here was memorable. Marclay, an American visual artist living in England, edited together clips from thousands of movies that mention or suggest time. His video runs for 24 hours, all in real time. If a scene from “3:10 to Yuma” flashes onto the screen, the watch on your wrist will say it’s 3:10. “The Clock” is mesmerizing on many different levels. Even though time is constantly before you on the screen — someone looking at a ticking clock or meeting under gonging Big Ben or rushing beneath a grand railway station clock — you’re not aware of its passage, and it’s possible to sit for hours, totally engrossed, waiting for what the next moment will bring.

Until June 5, the Garage has “New York Minute,” an exhibition of the work of 50 youthful American artists curated by Kathy Grayson, who grew up in Washington and now operates a gallery called The Hole in New York. On opening day in April, performance artist Terence Koh wandered through Red Square, covered in a blood-red tarp, his hands and feet painted red, and carrying red flowers. Police quickly materialized and informed him that such dress is not permitted in Moscow, where the squares remain resolutely, well, square.

Back at the Garage, with “New York Minute” celebrating the just-off-the-street energy of that city, Koh found a more appreciative audience. There, visitors were greeted by a New York police car hanging upside down from the ceiling, with a blackened disco ball attached (the work of Spencer Sweeney), columnlike rows of giant cast rubber bands (Martha Friedman) and paintings made out of chewing gum (Dan Colen.)

The Americans loved the Garage, and its progressive air gave them trouble figuring out the city around it. Grayson was transfixed by the dissonance between the former and the current Moscow. At the Pushkin Museum, the city’s largest and home to famous van Goghs and Picassos, she found peeling wallpaper and awkwardly hung works. But in a store near the Garage, she saw children’s birthday cards emblazoned with expensive cars or pictures of money, reflecting the modern get-rich culture. “Not one had a birthday cake or a puppy,” she said.

Moscow takes some work, said Rafael de Cardenas, an architect and former Calvin Klein designer who designed the “New York Minute” exhibition. You have to know where to go and dig a little to get at the good stuff, he said. (Friends filled the Americans in, and some later found themselves at the chichi club owned by Russian designer Denis Simachev, in a clubby neighborhood that also features Club Gogol.) Jim Drain, who along with Ara Peterson made brightly painted foam pinwheels for the exhibition, called it a weird Faberge egg of a place — with well-concealed secrets inside.

Barry McGee, a California graffiti writer who has crossed over into fine art, had wandered into the State Polytechnical Museum in a century-old building crammed with about 175,000 objects, including old televisions, computers and other objects. When he told me that they were displayed with a we-still-have-some-secrets-here-air, I knew I had to visit.

Don’t miss the row of spark plugs in the auto section. (My husband stared a long time at the aircraft and automobile engines, and he greatly admired the 1915 orange motorcycle from Indian Motorcycle in Springfield, Mass.) My favorite was the cafe, with its Soviet-era clock and selection of beet salads, but I also lingered over the telephone room, with its 1904 Moscow switchboard, 1980 fax (a controlled substance in that era) and relatively recent cellphones.

Put it on your list, I say. After all, what’s hipper than irony?