"I'm feeling like a kid in a candy shop," says conductor Alan Gilbert to his wife, cellist Kajsa -William-Olsson. "A very privileged kid." We are walking, through the soothingly empty halls of New York's Metropolitan Museum of Art, en route upstairs to one of Mr. Gilbert's favorite galleries, containing works by Jan Vermeer and other 17th-century Dutch painters. The museum is so quiet because it's a Monday, when the Met is closed except to special visitors. Mr. Gilbert is distinctly special: On Sept. 16 he opens his first season as music director of the New York Philharmonic, inheriting a mantle previously worn by such immortals as Arturo Toscanini, Bruno Walter and Leonard Bernstein, not to mention his immediate predecessors, Lorin Maazel, Kurt Masur and Zubin Mehta.