51st century & beyond
The TARDIS materializes on the fringes of the slightly shabby city, behind a cluster of trees and, ironically, the fifty-first century equivalent of a phone box, something like a high-powered sort of communications booth that's more likely to scan your retina than to politely request the drop of a fifty pence piece.
After a moment or two, the door of the blue police box opens and the Doctor steps out, shrugging into his brown overcoat. However, unlike has been the trend of late, the Time Lord isn't alone.
A young man steps out of the ship after the Doctor, dressed down in contrast to the alien in a pair of jeans and a button-down shirt with a jumper pulled over it. He looks around their surroundings, then turns to the Doctor with a questioning stare. "All of time and space," he states after a moment. "And you bring me to the fifty-first century equivalent of Splott?"
"Oh," the Doctor waves offhandedly. "Well, not my finest hour, but it wasn't my choice where she decided to settle down at. Ah well, allons-y, Mr. Jones!" He slides his hands into his pockets, then leads the way at a leisurely strolling pace for a large apartment building.
It seems like an infinity of walking (with the aforementioned Mr. Jones muttering about modern convenience not involving elevators or escalators) up stairs before they finally arrive outside a door, where the Doctor knocks.