The capital of this fascinating island, once known as Formosa (“beautiful island” in Portuguese), has a rich aboriginal, colonial and political history. Snap a selfie at the ornate, dragon-adorned Mengjia Longshang Temple or photograph the changing of the guard at Chiang Kai-Shek Memorial Hall, a must-see site. Experience 360-degree views of the city from the 91st floor observation deck of Taipei 101. Selfies and panaromic pics done, head off to shop for Taiwanese lacquerware, silk and fine art.