Originally a rundown accommodation in one of City 17's many apartment blocks, Nathan was housed her upon his arrival in City 17. He shared the apartment with at least 5 other citizens (two of them being the Consoling Couple and the place was occasionally raided by Civil Protection officers, trashed and missing doors.
Nathan ended up living at the apartment himself, presumably after the occupants were either arrested or killed by Metropolice as depicted in the first Half-Life 2 chapter Point Insertion. After the downfall of the Combine, Nathan continued living there and tidied the place up a bit.
Many came to live with Nathan at his apartment, including his friend Sarah Woods and then his girlfriend and daughter Chell and Samantha respectively. Sometimes Nathan would go long periods without living at the apartment and would find accommodation elsewhere, but would return to live at his apartment.
During the Race X's attempted invasion of earth the apartment was destroyed, much to Nathan's sadness. However it was later rebuilt exactly the way it was before.
The apartment was completely destroyed following the destruction of City 17 as a whole.