I am trying to find a sci fi short story about a young man who has never left the city. He decides to walk to find what lies beyond the city. The story describes the people, things & places he sees. At some point a woman/girl accompanies him although she doesn't understand why he wants to see what is beyond the city. Eventually, he ends up finding out that the city never ends just goes in a circle or maybe a huge block. He ends up back where he started. At the end of the story, the woman/girl stops to do some "work" and the man comes down a conveyor belt and she chops him up presumably for food. This may have been written during the Golden Age or during the New Wave of science fiction (pre-1970).
"The World as Will and Wallpaper", a 1973 short story by R. A. Lafferty (with title apparently inspired by Schopenhauer's The World as Will and Representation), which you may have read in one of these compilations. First published in the anthology Future City (Roger Elwood, ed.), it was reprinted in The Best Science Fiction of the Year #3 (Terry Carr, ed.) which you can borrow (for free but registration required) from the Internet Archive.
There is an old dictionary-encyclopedia that defines a City as ". . . a concentration of persons that is not economically self-sufficient." The dictionary-encyclopedia being an old one, however (and there is no other kind), is mistaken. The World City is economically self-sufficient.
It was William Morris who read this definition in the old book. William was a bookie, or readie, and he had read parts of several books. But now he had a thought. If all the books are old, then things may no longer be as the books indicate. I will go out and see what things are like today in the City. I will traverse as much of the City as my life allows me. I may even come to the Wood Beyond the World that my name-game ancestor described.
William has girl companions along the way:
Outside, William found a companion named Kandy Kalosh and they began to traverse the City that was the World. They began (it was no more than coincidence) at a marker set in stone that bore the words "Beginning of Stencil 35,352." The City tipped and tilted a bit, and they were on their way. Now this is what the City was like.
[. . . .]
In the morning, Kandy Kalosh wanted to return to her home even though it was nearly twenty blocks to the eastward. William watched her go without sorrow. He would get a westering girl to go with him on the lifelong exploration of the endlessly varied City. He might get a girl who was a talkie or even a readie, or bookie.
And he did. She was named Fairhair Farquhar, though she was actually dark of hair and of surface patina. But they started out in the early morning to attain (whether in a day or a lifetime) the Wood Beyond the World.
Among the many things William sees as he explores the City is the Chopper House:
William and Fairhair came to the great Chopper House at 20th Street. The two of them went in and worked for an hour in the Chopper House.
"You do not understand this, do you, little William?" Fairhair asked.
"Oh, I understand enough for me. I understand that it is everywhere different."
"Yes, I suppose you understand enough for you," Fairhair said with a touch of near sadness. (What they chopped up in the Chopper House was the ancients.) They went on and on along the strips and streets of the ever-changing city. They came to 21st Street and 22nd and 23rd. Even a writie could not write down all the marvels that were to be found at every street. It is sheer wonder to be a world traveler.
After they find the Wood Beyond the World, Fairhair leaves William:
"Run, William, run in the morning!" Fairhair cried, and she ran while William (confused from the night) shuffled after her.
"We must leave the Wood?" he asked.
"Of course you must leave the Wood. You want to see the whole world, so you cannot stay in one place. You go on, I go back. No, no, don't you look back or you'll be turned into a salt-wood tree."
"Stay with me, Fairhair."
"No, no, you want variety. I have been with you long enough. I have been guide and companion and pony to you. Now we part."
Fairhair went back. William was afraid to look after her. He was in the world beyond the Wood Beyond the World. He noticed though that the street was 1st Street and not 31st Street as he had expected.
William's third companion resembles the first one but is different:
"Is your name Kandy Kalosh?" he asked as quakingly as a one-legged kangaroo with the willies.
"The last thing I needed was a talkie," she said. "Of course it isn't. My name, which I have from my name-game ancestor, is Candy Calabash, not at all the same."
Finally, Candy takes William to the Chopper House:
"It's the same thing over and over and over again," William whimpered as she toted him along.
"Be quiet talkie," she said, but she said it with some affection.
They came to the great Chopper House on 20th Street. Candy carried William in and dumped him on a block there.
"He's become ancient," Candy told an attendant. "Boy, how he's become ancient!" It was more than she usually talked.
Then, as she was a fair-minded girl and as she had not worked any stint that day, she turned to and worked an hour in the Chopper House. (What they chopped up in the Chopper House was the ancients.) Why, there was William's head coming down the line! Candy smiled at it. She chopped it up with loving care, much more care than she usually took.
She'd have said something memorable and kind if she'd been a talkie.