The gates of the Citadel at Oldtown are flanked by a pair of Sphinxes, a male and a female:
Do we know anything about why and how they got to be there?
There are a few references throughout the books to statues of Valyrian sphinxes appearing in prominent places: outside the council chamber in King's Landing, outside the Citadel in Oldtown, and flanking a road in the Velvet Hills of Essos:
The next evening they came upon a huge Valyrian sphinx crouched beside the road. It had a dragon's body and a woman's face.
"A dragon queen," said Tyrion. "A pleasant omen."
"Her king is missing." Illyrio pointed out the smooth stone plinth on which the second sphinx once stood, now grown over with moss and flowering vines. "The horselords built wooden wheels beneath him and dragged him back to Vaes Dothrak."
-- A Dance with Dragons, chapter Tyrion II
They seem to be "a thing" in the world of Ice and Fire, built by powerful people in certain significant places.
Also, they are certainly associated with riddles just as in the real world:
"The dragon has three heads," [Alleras (nicknamed the Sphinx)] announced in his soft Dornish drawl.
"Is this a riddle?" Roone wanted to know. "Sphinxes always speak in riddles in the tales."
-- A Feast for Crows, Prologue
So it seems apposite enough to place sphinxes outside the Citadel, a place of academic study, fit for those who can solve riddles set by such creatures. In the real world, sphinxes are often seen as guardians, asking questions to test the intelligence of people seeking to enter a place. If the same is true in the world of Ice and Fire - and what little we know about sphinxes there does match with the stories in the real world - then it would make perfect sense to place them outside the Citadel.