Built in 1741 by Sultan Mahmut I, and untouched since then, the Caalolu Hamam is the city’s most famous and one of its most attractive.  Ten minutes up the road from the Hagia Sophia, it’s brought in tourists for centuries, including, apparently, Tony Curtis, famous for his enjoyment of baths, King Edward VIII, Kaiser Wilhelm, Florence Nightingale and Franz Liszt. Though the service can be mediocre, this is a great hamam to try.