Science fiction story with a girl with silver eye, trying to find someone at some arcades... probably taken place at japan... something involves artificial organs... a teenager programmer staying at the rooftop of a building in the city...
This very much looks to be William Gibson's Neuromancer:
Most of Gibson's stories take place in Japan, or have a Japanese link. Neuromancer starts off in Chiba City, a suburb of Tokyo.
Girl with Silver Eyes
Here's the description of Molly Millions, one of the main protagonists:
She shook her head. He realized that the glasses were surgically inset, sealing her sockets. The silver lenses seemed to grow from smooth pale skin above her cheekbones, framed by dark hair cut in a rough shag.
Searching in an Arcade
Near the start of the novel, Case, the main protagonist, is looking for Linda, his girlfriend, whom he met at an arcade:
He'd found her, one rainy night, in an arcade. Under bright ghosts burning through a blue haze of cigarette smoke, holograms of Wizard's Castle, Tank War Europa, the New York skyline.... And now he remembered her that way, her face bathed in restless laser light, features reduced to a code: her cheekbones flaring scarlet as Wizard's Castle burned, forehead drenched with azure when Munich fell to the Tank War, mouth touched with hot gold as a gliding cursor struck sparks from the wall of a skyscraper canyon.
Case is a hacker, but starts the novel off with his nervous system shot, unable to connect to the Matrix. He is repaired by private surgeons, which included extensive neurosurgery and a new, artifical pancreas, which had the (unfortunate for Case) property of making most drugs ineffective.
After Case is fixed up, neurologically, he's recovering in a loft in an industrial building, high above the Sprawl, an American city, and is given a shiny new cyberspace deck to go online with. He's no teenager, but it seems close enough for your recollections.