During Shakespeare's day, the theatres were located across the Thames from the City of London. This was also the red light district. The rents for this area were paid to the Bishop of Winchester, thus the term Winchester geese for prostitutes.
Even during Shakespeare's day, the area was notorious for debauchery, often involving prominent members of Elizabethan society.
Shakespeare was smart enough to place his play in a foreign city, Vienna, rather than contemporary London. In this way, he could hold the mirror up to nature, but if he was called out about it, he had only to point to the location.