unlost horizon - View this location on map to glimpse the private passions of the late reclusive billionaire doris duke, take a peek at shangri la on the other side of diamond head. the two-hour tours of the islamic museum on her oceanfront estate begin and end at the honolulu academy of arts (808-532-8701; reservations required; www.shangrilahawaii.org). a 15-minute shuttle ride takes you to the site, where a mughal garden quiets the mind and 13th-century persian tiles line the walls of the central courtyard. the 8th- to 20th-century artifacts are integrated into the architecture, so you can stand at a 13th-century prayer niche, called a mihrab, then sit in the gleaming turkish room, where ms. duke, a tobacco heiress, entertained guests after dinner. NYT 900 south beretania street, Honolulu, HI Hisotrical, Cultural

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