Galata Tower, Turkey

The cylindrical Galata Tower stands sentry over the approach to 'new' İstanbul. Constructed in 1348, it was the tallest structure in the city for centuries, and it still dominates the skyline north of the Golden Horn. Its vertiginous upper balcony offers 360-degree views of the city, but we're not convinced that the view (though spectacular) justifies the steep admission cost.
Be warned that queues can be long and the viewing balcony can get horribly overcrowded. An elevator goes most of the way to the top, but there is one flight of stairs to climb.