Tobacco heiress Doris Duke's estate, Shangri La, was built on five seaside acres in Honolulu's exclusive Black Point between 1936 and 1939. Though its name might suggest otherwise, the house is an Arabian Nights fantasy, and it's now open to the public (866/385-3849; tours $25 per person, reservations essential). Duke, who had a passion for surfing (she owned 14 boards), was equally enthralled by Islamic art, and the house is filled with treasures she collected on her travels: antique mother-of-pearl chests from Syria, a 12th-century Iranian prayer niche, Indian mosaic panels. For a glimpse of the Hawaii Duke loved, check out the Hawaii State Art Museum (250 S. Hotel St.; 808/586-0900), with its bronze sculptures of the demigod Maui, and the Luce Pavilion, the new wing of the Honolulu Academy of Arts (900 S. Beretania St.; 808/532-8700), where you'll see sketches dating back to the time of Captain Cook.