I'm trying to find a book about a city built on the side of an infinite wall - infinitely tall as well as infinitely long. There was a picture of it on the cover. The city is built on platforms jutting out, and if you fell off, you'd be gone forever. Unfortunately, I can't remember the title, the author, the publisher or anything else but the setting, but I think the plot might have been a detective story.
This sounds like On by Adam Roberts. The protagonist, Tighe, grows up in a village perched on a series of rocks/platforms sticking out from the infinite wall. At one point he falls off, luckily landing on the top of a hot-air ballon several miles below, where he joins a city.
At the end, we discover:
that this is the future of our world, but overuse of some sort of technology made gravity turn sideways, so that the "wall" is actually the ground of the planet and the platforms are hills and remnants of buildings from our time.
One cover shows Tighe climbing the wall.
I think this is Stone and Sky by Graham Edwards.
The book, as well as its sequels, follows the adventures of British historian and naturalist Jonah Lightfoot, who is caught in the eruption of Krakatoa in 1883. The blast transports him and American runaway Annie West into a vertical world consisting of a seemingly infinite wall populated by crumbling civilisations, weird creatures, and sentient dragons. No one knows where the wall begins or ends, and no one dares to climb to its top or fall to its base.
This world is called Amara, and it is a place deeply entwined with our own world. Throughout the books Jonah and his companions traverse the world and uncover its many mysteries. The true nature of Amara is fully revealed in the second book of the trilogy, Stone and Sea.