Beijing gracefully balances old and new, from crumbling nooks and crannies to contemporary constructions and traditional flavors to avant-garde techniques. Young, progressive, antiquated, and aged — all living together in an ancient city. Somehow it just works. You have to see it to believe it.Rest/IngestSituated on Kunming Lake, the Aman at Summer Palace is in a sprawling complex of palaces, pavilions, towers, and bridges. Aman’s rooms have individual courtyards, opium beds, and giant bathrooms with seasonal spa products. Pop down to the wine cellar and sample vino varietals, courtesy of China’s recent wine boom. Tastings range from a Bordeaux blend grown on the slopes of Mount Helen in Ningxia to a light, floral muscat from Liaoning. The Opposite House is pretty much the opposite (ha!) of Aman: hypermodern; clean lines; lots of wood; and spacious, loftlike rooms.Chew/ViewLeave your squeamishness at the door of Dadong Roast Duck. Hands down the best spot serving traditional Peking duck, Dadong’s birds hang from hooks, waiting for pin-striped cooks to shove them into a brick oven and bake them to crispy perfection. Top the meat with dozens of pickled sides and ask your server to help you fold it all into the accompanying thin pancakes (22 Dongsishitiao, Dongcheng +86-5169-0328). At year-old Capital M, scenesters steal some of the city’s best views (Qianmen Gate, Tian’anmen Square) while sipping afternoon tea or nibbling on signature European dishes (the pavlova is a must). Cha-Ching/BlingBeijing’s mix of old and new makes for an awesomely diverse shopping experience. German designer Kathrin von Rechenberg uses teasilk (a material worn by the ancients that involves a 30-step dye process) to create structured wraparound pants and kimono-sleeve tops. Affectionately referred to as the Dirt Market by locals (it’s cheap and charmingly cluttered), Panjiayuan’s weekend flea market is chockful of odds and ends like Ming pottery, opium pipes, and jade (southwest of the Panjiayuan Bridge at East Third Ring South Road, Chaoyang). Get your bling fix at jeweler Paloma Sanchez’s Nali Patio boutique. Her trademark: rough and uncut quartz, amethyst, and fluorite. Browse local designer Jian Ping’s high-end, ancestral-cut kimonos; puff-sleeve shirts; fisherman’s pants; and Chinese knot buttons in a modern, serene space (110-2 Nanluoguxiang Hutong, Dongcheng; +86-6402-4779).Tour/MoreLocated in a converted Soviet electronics factory, Ullens Center for Contemporary Art’s exhibits offer commentary on consumerism and globalization. Experience the Great Wall without the heavy crowds by heading 90 minutes northeast to Mutianyu, a section known for its ancient watchtowers. Eat an organic lunch at The Schoolhouse, part of Mutianyu’s sustainable tourism effort. Then it’s back to the big city.Photos: Courtesy of Aman Resorts; Marcella Echavarria; Courtesy of Paloma Sanchez; Courtesy of Ullens Center for Contemporary ArtUp to 80% off ChaikenSF designer Julie Chaiken is famous for her expertly fitted slacks. Load up on those and more (sleek LBDs, cashmere cardis, swanky silk tops) while they’re up to 80 percent off on our sample sale site.