Surgery is a location in Stray where Companions can replace their body parts, not counting the head (it can also be replaced in a Barbershop). Such locations can be found both in Slums and in Midtown.
You can't enter the Surgery, but you can recognize it by the red-and-white sign on the door with the inscription "Surgery 7/7" (7/7 is the French way to write "7 days a week").
Slums[]
Slums Surgery
The Surgery in the Slums is not far from the Super Spirit Laundry, near the corner where Zoe is sitting. There is a grille nearby (once there was a shop showcase?), and there is a sign "SHOP" above the door.
It is not known who is the surgeon there, but the Cat can scratch the Door and listen to what is happening behind it: "Please, don't act like a child. I'm not gonna hurt you." Apparently, some Companions are afraid of some medical procedures, just like Humans.
Midtown[]
Midtown Surgery
The Surgery in Midtown is in the alley behind the Nightclub that Albert sweeps. There are old parts of the Companions' bodies and some equipment lying near the door. The Cat can go up to the balcony above the door and hear a complaint from the neighbors from there: "I don't know what the downstairs neighbours are up to. I keep hearing buzzsaw and hammer noises!".
After the Cat visits Neco Corporation factory and Clementine's Midtown apartment, and returns to the alley to go to the Nightclub, he will meet a street surgeon named Jameston, who is sitting near the door and nervously looking around, holding the head of one of their patients on their lap. If you talk to them, they will scare the cat: "You have no business here, unless you want your legs replaced by something more... fancy, which you don't! So get lost!", "What again?! Are you working for the Sentinels? I said get lost!". They may be conducting clandestine activities.