The City and Its Uncertain Walls by Haruki Murakami

When a young man's girlfriend mysteriously vanishes, he sets his heart on finding the imaginary city where her true self lives. His search will lead him to take a job in a remote library with mysteries of its own. When he finally makes it to the walled city, a shadowless place of horned beasts and willow trees, he finds his beloved working in a different library - a dream library. But she has no memory of their life together in the other world and, as the lines between reality and fantasy start to blur, he must decide what he's willing to lose.