When I meet Patrick Lee, director of art behemoth Frieze Seoul , the first café he proposes we try has vanished, its façade demolished. “This café was just here,” he says, disoriented but not at all surprised. “It was here the last time I was on this street. You see, this is what happens in Seoul.” In the city's vibrant historical center, hanoks —the traditional curved-roof wood houses that give Seoul its distinctive heart-stopping skyline—are jammed next to sleek art galleries, fashionable glasses shops, and pop-up boutiques. And my God, the cafés. How to convey the love for coffee in this high-octane, thrilling city of late-night barbershops and 4 a.m. Tuesday karaoke? Seoul bursts with, at some estimates, more than 15,000 cafés, many of them freshly opened, and the number keeps escalating. Lee and I grab coffee from a different café, then queue outside Art Sonje Center , which has been one of the city's most influential private art museums since it was founded in 1998.…