As the capital of Russia, Moscow is appropriately sprawling, a fast paced metropolis full of the contradictions so apparent in the country’s culture. Massive, bronze statues of Soviet workers tower over people wearing inflatable sumo wrestling outfits and passing out fliers for sushi restaurants; the subway system’s ornate ceiling mosaics watch over dogs getting on and off the trains; and teenagers with iPhones juggle texts and video game applications as they walk past old women—the last of the Soviet generation—begging for change. It’s a uniquely strange urban environment, and as such it deserves a look beyond the standard tourist paths—if you’re in for a little bit of adventure, here’s a good idea of where to start:

Red Square: OK, so this is not exactly off the beaten path, but any visit to Moscow is not complete without a visit here. The place is overrun with tourists, but that shouldn’t take anything away from the memories infused in the cobblestone courts and massive walls of The Kremlin palace. In terms of aesthetics, this may be the most glaring contradiction contained in the city: directly across the square from Lenin’s tomb—where you can pay 150 rubles (roughly $5) to be hustled in and out of a dark room to see the highly embalmed body of the Soviet leader—sits GUM, an enormous building full of designer boutiques (Louis Vuitton, Prada, etc).

VDNKh (All-State Russian Museum): This gigantic park is full of the aforementioned Soviet statues, along with intricate gold fountains and enough attractions to put Coney Island to shame. A museum about the history of torture is just a hop, skip and a jump away from a cat exhibition, which essentially allows visitors to pet a bunch of housecats. Just before the entrance is the Aerospace Museum, which boasts one of Moscow’s tallest monuments—a tribute to the Soviet Union’s brave cosmonauts—and a model of the universe made out of steel.

Museum of Soviet Arcade Games: This is one of the city’s best-kept secrets, a treasure trove of forgotten technology lovingly maintained by a few interesting souls at the Moscow State Technical Institute. Open very rarely (or by appointment), the museum offers visitors a look at gaming behind the Iron Curtain, when Russian folk tales and turnip knowledge alike was transformed into crude digital designs, and the handheld Playstations so frequently seen today in the metro were not even the stuff of daydreams.

Akuly: If you’re in town on a weekend, get yourself either to Pushkin Square or the fountain area just outside the Novokuznetskaya metro station, because Moscow’s hardest-working street band, Akuly ("sharks”) plays regularly for an extremely mixed crowd. Find businesswomen blowing off steam with a beer (or three or four), homeless drunks, policemen, young couples, old men and even the ubiquitous stray dog—Everyone in attendance can usually find their groove to a few songs in the thousands that make up Akuly's repertoire. The band plays every night somewhere in Moscow, so if you don't make the weekend shows (which usually start around 6 p.m. when the weather is warm), you're bound to find them somewhere else.

Proyekt O.G.I.: After a long day of statues, gaming, you can find food, drink and live music at one of Moscow's most (literally) underground clubs. The place is fairly tame in the early evening, with rock bands most nights and a good menu of bar food, but after midnight things really start hopping once the vodka starts flowing. Don't let the gruff doormen faze you, that's just part of the city's social landscape.

Travel tips: If you are arriving at any of the city's airports, follow the signs for the Aeroexpress train, which will cost 300 rubles ($10) for a 45-minute ride to the center of the city and will drop you off at a metro station. If you do take a cab, don't get pulled into a conversation with a cab driver, as you'll be paying an accent tax that can run your trip to the center close to $50 and get you ensnared in the city's notorious traffic. Once you reach the metro, things can be a bit confusing if you don't speak Russian, but the system is cheap (less than $1 per ride) and incredibly fast (trains come and go every two minutes).